Data processing device and data processing method

ABSTRACT

The present technology relates to a data processing device and a data processing method which can ensure high communication quality in data transmission using LDPC codes. 
     In group-wise interleaving, an LDPC code having a code length N of 64800 bits and a coding rate r of 11/15 is interleaved in a unit of a bit group of 360 bits. In group-wise deinterleaving, a sequence of bit groups of the LDPC code which has been subjected to the group-wise interleaving is returned to an original sequence. The present technology can be applied to, for example, a case in which data transmission is performed using LDPC codes.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/993,269, filed May 30, 2018, which is a continuation of U.S.Application No. 15/117,782, filed Aug. 10, 2016, which is a NationalStage application of PCT/JP2015/053184, filed Feb. 5, 2015 and claimsthe benefit of priority under 35 U.S.C. § 119 of Japanese ApplicationNo. 2014-030015, filed Feb. 19, 2014. The entire contents of each of theabove-identified applications are incorporated herein by reference.

TECHNICAL FIELD

The present technology relates to a data processing device and a dataprocessing method, and more particularly, to a data processing deviceand a data processing method which can ensure high communication qualityin data transmission using, for example, an LDPC code.

BACKGROUND ART

Some of information used in the specification and the drawings isprovided by Samsung Electronics Co., Ltd. (hereinafter, referred to asSamsung), LG Electronics Inc., NERC, and CRC/ETRI (which is clarified inthe drawings).

A low density parity check (LDPC) code has a high error correctioncapability and has been widely adopted in transmission systems fordigital broadcasting, for example, Digital Video Broadcasting (DVB)-S.2,DVB-T.2, and DVB-C.2 used in Europe, and Advanced Television SystemsCommittee (ATSC) 3.0 used in the U.S. (for example, see Non-PatentDocument 1).

The recent study shows that the performance of an LDPC code becomescloser to a Shannon limit as the code length thereof becomes larger,similar to a turbo code. The LDPC code has the property that theshortest distance is proportional to the code length. Therefore, theLDPC code has the advantages that block error probabilitycharacteristics are excellent and a so-called error floor phenomenonwhich is observed in the decoding characteristics of, for example, aturbo code rarely occurs.

CITATION LIST Non-Patent Document

Non-Patent Document 1: DVB-S.2: ETSI EN 302 307 V1.2.1 (2009-08)

SUMMARY OF THE INVENTION Problems to be Solved by the Invention

In data transmission using LDPC codes, for example, an LDPC code servesas a symbol (changes to a symbol) of quadrature modulation (digitalmodulation), such as quadrature phase shift keying (QPSK), and thesymbol is mapped to a signal point of the quadrature modulation and istransmitted.

The data transmission using LDPC codes has come into widespread use andthere has been a demand for ensuring high communication (transmission)quality.

The present technology has been made in view of the above-mentionedproblems and an objective of the present technology is to ensure highcommunication quality in data transmission using LDPC codes.

Solutions to Problems

A first data processing device/method according to the presenttechnology includes: a coding unit/step that performs LDPC coding on thebasis of a parity check matrix of an LDPC code having a code length N of64800 bits and a coding rate r of 11/15; a group-wise interleavingunit/step that performs group-wise interleaving which interleaves theLDPC code in a unit of a bit group of 360 bits; and a mapping unit/stepthat maps the LDPC code to any one of four signal points which aredetermined by a modulation method in a unit of 2 bits.

In the group-wise interleaving, an (i+1)-th bit group from a head of theLDPC code is set as a bit group i, an (i+1)-th bit group from a head ofthe LDPC code is set as a bit group i and a sequence of bit groups 0 to179 of the 64800-bit LDPC code is interleaved into a sequence of thefollowing bit groups.

0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107,31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129,52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97,33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17,15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130,56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45,78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96,32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149,151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177,179

The LDPC code includes information bits and parity bits. The paritycheck matrix includes an information matrix portion corresponding to theinformation bits and a parity matrix portion corresponding to the paritybits. The information matrix portion is represented by a parity checkmatrix initial value table. The parity check matrix initial value tableindicates positions of elements “1” in the information matrix portionfor every 360 columns and includes the following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

In the first data processing device/method, the LDPC coding is performedon the basis of the parity check matrix of the LDPC code having a codelength N of 64800 bits and a coding rate r of 11/15. The group-wiseinterleaving which interleaves the LDPC code in a unit of a bit group of360 bits is performed. Then, the LDPC code is mapped to any one of foursignal points which are determined by the modulation method in a unit of2 bits. In the group-wise interleaving, the (i+1)-th bit group from thehead of the LDPC code is set as the bit group i and a sequence of bitgroups 0 to 179 of the 64800-bit LDPC code is interleaved into asequence of the following bit groups.

0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107,31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129,52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97,33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17,15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130,56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45,78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96,32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149,151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177,179

The LDPC code includes the information bits and the parity bits. Theparity check matrix includes the information matrix portioncorresponding to the information bits and the parity matrix portioncorresponding to the parity bits. The information matrix portion isrepresented by the parity check matrix initial value table. The paritycheck matrix initial value table indicates the positions of the elements“1” in the information matrix portion for every 360 columns and includesthe following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

A second data processing device/method according to the presenttechnology includes: a group-wise deinterleaving unit/step that returnsa sequence of an LDPC code, which has been subjected to group-wiseinterleaving and is obtained from data transmitted from a transmittingdevice, to an original sequence. The transmitting device includes: acoding unit that performs LDPC coding on the basis of a parity checkmatrix of the LDPC code having a code length N of 64800 bits and acoding rate r of 11/15; a group-wise interleaving unit that performs thegroup-wise interleaving which interleaves the LDPC code in a unit of abit group of 360 bits; and a mapping unit that maps the LDPC code to anyone of four signal points which are determined by a modulation method ina unit of 2 bits. In the group-wise interleaving, an (i+1)-th bit groupfrom a head of the LDPC code is set as a bit group i and a sequence ofbit groups 0 to 179 of the 64800-bit LDPC code is interleaved into asequence of the following bit groups.

0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107,31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129,52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97,33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17,15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130,56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45,78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96,32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149,151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177,179

The LDPC code includes information bits and parity bits. The paritycheck matrix includes an information matrix portion corresponding to theinformation bits and a parity matrix portion corresponding to the paritybits. The information matrix portion is represented by a parity checkmatrix initial value table. The parity check matrix initial value tableindicates positions of elements “1” in the information matrix portionfor every 360 columns and includes the following. 696 989 1238 3091 31163738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

In the second data processing device/method, the transmitting deviceincludes: the coding unit that performs LDPC coding on the basis of theparity check matrix of the LDPC code having a code length N of 64800bits and a coding rate r of 11/15; the group-wise interleaving unit thatperforms the group-wise interleaving which interleaves the LDPC code ina unit of a bit group of 360 bits; and the mapping unit that maps theLDPC code to any one of four signal points which are determined by themodulation method in a unit of 2 bits.

In the group-wise interleaving, the (i+1)-th bit group from the head ofthe LDPC code is set as the bit group i and a sequence of bit groups 0to 179 of the 64800-bit LDPC code is interleaved into a sequence of thefollowing bit groups.

0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107,31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129,52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97,33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17,15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130,56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45,78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96,32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149,151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177,179

LDPC code includes the information bits and the parity bits. The paritycheck matrix includes the information matrix portion corresponding tothe information bits and the parity matrix portion corresponding to theparity bits. The information matrix portion is represented by the paritycheck matrix initial value table. The parity check matrix initial valuetable indicates positions of elements “1” in the information matrixportion for every 360 columns and includes the following. A sequence ofthe bit groups of the LDPC code, which has been subjected to thegroup-wise interleaving and is obtained from the data transmitted fromthe transmitting device, is returned to the original sequence.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

88 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 1713717268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

A third data processing device/method according to the presenttechnology includes: a coding unit/step that performs LDPC coding on thebasis of a parity check matrix of an LDPC code having a code length N of64800 bits and a coding rate r of 11/15; a group-wise interleavingunit/step that performs group-wise interleaving which interleaves theLDPC code in a unit of a bit group of 360 bits; and a mapping unit/stepthat maps the LDPC code to any one of 16 signal points which aredetermined by a modulation method in a unit of 4 bits. In the group-wiseinterleaving, an (i+1)-th bit group from a head of the LDPC code is setas a bit group i and a sequence of bit groups 0 to 179 of the 64800-bitLDPC code is interleaved into a sequence of the following bit groups.

21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73,100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114,132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10,13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95,86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141,145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82,32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70,91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158,162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131,33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60,67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175,179

The LDPC code includes information bits and parity bits. The paritycheck matrix includes an information matrix portion corresponding to theinformation bits and a parity matrix portion corresponding to the paritybits. The information matrix portion is represented by a parity checkmatrix initial value table. The parity check matrix initial value tableindicates positions of elements “1” in the information matrix portionfor every 360 columns and includes the following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

In the third data processing device/method, the LDPC coding is performedon the basis of the parity check matrix of the LDPC code having a codelength N of 64800 bits and a coding rate r of 11/15. The group-wiseinterleaving which interleaves the LDPC code in a unit of a bit group of360 bits is performed. Then, the LDPC code is mapped to any one of 16signal points which are determined by the modulation method in a unit of4 bits. In the group-wise interleaving, the (i+1)-th bit group from thehead of the LDPC code is set as the bit group i and a sequence of bitgroups 0 to 179 of the 64800-bit LDPC code is interleaved into asequence of the following bit groups.

21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73,100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114,132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10,13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95,86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141,145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82,32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70,91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158,162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131,33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60,67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175,179

The LDPC code includes the information bits and the parity bits. Theparity check matrix includes the information matrix portioncorresponding to the information bits and the parity matrix portioncorresponding to the parity bits. The information matrix portion isrepresented by the parity check matrix initial value table. The paritycheck matrix initial value table indicates the positions of the elements“1” in the information matrix portion for every 360 columns and includesthe following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090 981 1205 4400 6410 11003 13319 13405 14695 15846 1629716492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

A fourth data processing device/method to the present technologyincludes a group-wise deinterleaving unit/step that returns a sequenceof an LDPC code, which has been subjected to group-wise interleaving andis obtained from data transmitted from a transmitting device, to anoriginal sequence. The transmitting device includes: a coding unit thatperforms LDPC coding on the basis of a parity check matrix of the LDPCcode having a code length N of 64800 bits and a coding rate r of 11/15;a group-wise interleaving unit that performs the group-wise interleavingwhich interleaves the LDPC code in a unit of a bit group of 360 bits;and a mapping unit that maps the LDPC code to any one of 16 signalpoints which are determined by a modulation method in a unit of 4 bits.In the group-wise interleaving, an (i+1)-th bit group from a head of theLDPC code is set as a bit group i and a sequence of bit groups 0 to 179of the 64800-bit LDPC code is interleaved into a sequence of thefollowing bit groups.

21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73,100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114,132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10,13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95,86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141,145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82,32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70,91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158,162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131,33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60,67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175,179

The LDPC code includes information bits and parity bits. The paritycheck matrix includes an information matrix portion corresponding to theinformation bits and a parity matrix portion corresponding to the paritybits. The information matrix portion is represented by a parity checkmatrix initial value table. The parity check matrix initial value tableindicates positions of elements “1” in the information matrix portionfor every 360 columns and includes the following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

In the fourth data processing device/method, the transmitting deviceincludes: the coding unit that performs LDPC coding on the basis of theparity check matrix of the LDPC code having a code length N of 64800bits and a coding rate r of 11/15; the group-wise interleaving unit thatperforms the group-wise interleaving which interleaves the LDPC code ina unit of a bit group of 360 bits; and the mapping unit that maps theLDPC code to any one of 16 signal points which are determined by themodulation method in a unit of 4 bits. In the group-wise interleaving,the (i+1)-th bit group from the head of the LDPC code is set as the bitgroup i and a sequence of bit groups 0 to 179 of the 64800-bit LDPC codeis interleaved into a sequence of the following bit groups.

21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73,100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114,132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10,13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95,86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141,145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82,32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70,91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158,162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131,33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60,67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175,179

The LDPC code includes the information bits and the parity bits. Theparity check matrix includes the information matrix portioncorresponding to the information bits and the parity matrix portioncorresponding to the parity bits. The information matrix portion isrepresented by the parity check matrix initial value table. The paritycheck matrix initial value table indicates positions of elements “1” inthe information matrix portion for every 360 columns and includes thefollowing. A sequence of the bit groups of the LDPC code, which has beensubjected to the group-wise interleaving and is obtained from the datatransmitted from the transmitting device, is returned to the originalsequence.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

A fifth data processing device/method according to the presenttechnology includes: a coding unit/step that performs LDPC coding on thebasis of a parity check matrix of an LDPC code having a code length N of64800 bits and a coding rate r of 11/15; a group-wise interleavingunit/step that performs group-wise interleaving which interleaves theLDPC code in a unit of a bit group of 360 bits; and a mapping unit/stepthat maps the LDPC code to any one of 64 signal points which aredetermined by a modulation method in a unit of 6 bits. In the group-wiseinterleaving, an (i+1)-th bit group from a head of the LDPC code is setas a bit group i and a sequence of bit groups 0 to 179 of the 64800-bitLDPC code is interleaved into a sequence of the following bit groups.

12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72,116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9,5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55,103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28,104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125,58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101,94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135,141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47,80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148,154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42,114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161,167, 173, 179

The LDPC code includes information bits and parity bits. The paritycheck matrix includes an information matrix portion corresponding to theinformation bits and a parity matrix portion corresponding to the paritybits. The information matrix portion is represented by a parity checkmatrix initial value table. The parity check matrix initial value tableindicates positions of elements “1” in the information matrix portionfor every 360 columns and includes the following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

In the fifth data processing device/method, the LDPC coding is performedon the basis of the parity check matrix of the LDPC code having a codelength N of 64800 bits and a coding rate r of 11/15. The group-wiseinterleaving which interleaves the LDPC code in a unit of a bit group of360 bits is performed. Then, the LDPC code is mapped to any one of 64signal points which are determined by the modulation method in a unit of6 bits. In the group-wise interleaving, the (i+1)-th bit group from thehead of the LDPC code is set as the bit group i and a sequence of bitgroups 0 to 179 of the 64800-bit LDPC code is interleaved into asequence of the following bit groups.

12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72,116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9,5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55,103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28,104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125,58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101,94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135,141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47,80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148,154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42,114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161,167, 173, 179

The LDPC code includes the information bits and the parity bits. Theparity check matrix includes the information matrix portioncorresponding to the information bits and the parity matrix portioncorresponding to the parity bits. The information matrix portion isrepresented by the parity check matrix initial value table. The paritycheck matrix initial value table indicates the positions of the elements“1” in the information matrix portion for every 360 columns and includesthe following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

A sixth data processing device/method according to the presenttechnology includes a group-wise deinterleaving unit/step that returns asequence of an LDPC code, which has been subjected to group-wiseinterleaving and is obtained from data transmitted from a transmittingdevice, to an original sequence. The transmitting device includes: acoding unit that performs LDPC coding on the basis of a parity checkmatrix of the LDPC code having a code length N of 64800 bits and acoding rate r of 11/15; a group-wise interleaving unit that performs thegroup-wise interleaving which interleaves the LDPC code in a unit of abit group of 360 bits; and a mapping unit that maps the LDPC code to anyone of 64 signal points which are determined by a modulation method in aunit of 6 bits. In the group-wise interleaving, an (i+1)-th bit groupfrom a head of the LDPC code is set as a bit group i and a sequence ofbit groups 0 to 179 of the 64800-bit LDPC code is interleaved into asequence of the following bit groups.

12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72,116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9,5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55,103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28,104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125,58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101,94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135,141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47,80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148,154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42,114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161,167, 173, 179

The LDPC code includes information bits and parity bits. The paritycheck matrix includes an information matrix portion corresponding to theinformation bits and a parity matrix portion corresponding to the paritybits. The information matrix portion is represented by a parity checkmatrix initial value table. The parity check matrix initial value tableindicates positions of elements “1” in the information matrix portionfor every 360 columns and includes the following.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

In the sixth data processing device/method, the transmitting deviceincludes: the coding unit that performs LDPC coding on the basis of theparity check matrix of the LDPC code having a code length N of 64800bits and a coding rate r of 11/15; the group-wise interleaving unit thatperforms the group-wise interleaving which interleaves the LDPC code ina unit of a bit group of 360 bits; and the mapping unit that maps theLDPC code to any one of 64 signal points which are determined by themodulation method in a unit of 6 bits. In the group-wise interleaving,the (i+1)-th bit group from the head of the LDPC code is set as the bitgroup i and a sequence of bit groups 0 to 179 of the 64800-bit LDPC codeis interleaved into a sequence of the following bit groups.

12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72,116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9,5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55,103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28,104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125,58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101,94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135,141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47,80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148,154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42,114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161,167, 173, 179

The LDPC code includes the information bits and the parity bits. Theparity check matrix includes the information matrix portioncorresponding to the information bits and the parity matrix portioncorresponding to the parity bits. The information matrix portion isrepresented by the parity check matrix initial value table. The paritycheck matrix initial value table indicates positions of elements “1” inthe information matrix portion for every 360 columns and includes thefollowing. A sequence of the bit groups of the LDPC code, which has beensubjected to the group-wise interleaving and is obtained from the datatransmitted from the transmitting device, is returned to the originalsequence.

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 1645616912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 1691617137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 1671417157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 1424716717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 1663217040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 1713217226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 1602416812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 1531116391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 1696117033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 1649316690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 1661616862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 1705017060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 1679916833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 1717117179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 1682517112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 1710217251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 1520215335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 1703017103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 1704417250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 1717717238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 1703717062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255

The data processing device may be an independent device or an internalblock forming one device.

Effects of the Invention

According to the present technology, it is possible to ensure highcommunication quality in data transmission using LDPC codes.

The effects described herein are not necessarily limited and may be anyeffect described in the present disclosure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram illustrating a parity check matrix H of an LDPCcode.

FIG. 2 is a flowchart illustrating an LDPC code decoding process.

FIG. 3 is a diagram illustrating an example of a parity check matrix ofan LDPC code.

FIG. 4 is a diagram illustrating an example of a Tanner graph of theparity check matrix.

FIG. 5 is a diagram illustrating an example of a variable node.

FIG. 6 is a diagram illustrating an example of a check node.

FIG. 7 is a diagram illustrating an example of the structure of anembodiment of a transmission system to which the present technology isapplied.

FIG. 8 is a block diagram illustrating an example of the structure of atransmitting device 11.

FIG. 9 is a block diagram illustrating an example of the structure of abit interleaver 116.

FIG. 10 is a diagram illustrating an example of a parity check matrix.

FIG. 11 is a diagram illustrating an example of a parity matrix.

FIG. 12 is a diagram illustrating a parity check matrix of an LDPC codedefined by a DVB-T.2 standard.

FIG. 13 is a diagram illustrating the parity check matrix of the LDPCcode defined by the DVB-T.2 standard.

FIG. 14 is a diagram illustrating an example of a

Tanner graph for the decoding of an LDPC code.

FIG. 15 is a diagram illustrating an example of a parity matrix H_(T)having a dual diagonal structure and a Tanner graph corresponding to theparity matrix H_(T).

FIG. 16 is a diagram illustrating an example of a parity matrix H_(T) ofa parity check matrix H corresponding to an LDPC code subjected toparity interleaving.

FIG. 17 is a flowchart illustrating an example of a process performed bythe bit interleaver 116 and a mapper 117.

FIG. 18 is a block diagram illustrating an example of the structure ofan LDPC encoder 115.

FIG. 19 is a flowchart illustrating an example of the process of theLDPC encoder 115.

FIG. 20 is a diagram illustrating an example of a parity check matrixinitial value table for a parity check matrix having a coding rate of1/4 and a code length of 16200.

FIG. 21 is a diagram illustrating a method for calculating a paritycheck matrix H from the parity check matrix initial value table.

FIG. 22 is a diagram illustrating the structure of a parity checkmatrix.

FIG. 23 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 24 is a diagram illustrating an A matrix which is generated fromthe parity check matrix initial value table.

FIG. 25 is a diagram illustrating parity interleaving for a B matrix.

FIG. 26 is a diagram illustrating a C matrix which is generated from theparity check matrix initial value table.

FIG. 27 is a diagram illustrating parity interleaving for a D matrix.

FIG. 28 is a diagram illustrating a parity check matrix obtained byperforming column permutation as parity deinterleaving, which returns asequence subjected to parity interleaving to an original sequence, forthe parity check matrix.

FIG. 29 is a diagram illustrating a transformed parity check matrixobtained by performing row permutation for the parity check matrix.

FIG. 30 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 31 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 32 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 33 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 34 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 35 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 36 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 37 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 38 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 39 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 40 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 41 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 42 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 43 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 44 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 45 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 46 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 47 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 48 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 49 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 50 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 51 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 52 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 53 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 54 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 55 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 56 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 57 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 58 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 59 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 60 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 61 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 62 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 63 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 64 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 65 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 66 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 67 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 68 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 69 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 70 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 71 is a diagram illustrating an example of the parity check matrixinitial value table.

FIG. 72 is a diagram illustrating the example of the parity check matrixinitial value table.

FIG. 73 is a diagram illustrating an example of a Tanner graph of anensemble of a degree sequence having a column weight of 3 and a rowweight of 6.

FIG. 74 is a diagram illustrating an example of a Tanner graph of amulti-edge-type ensemble.

FIG. 75 is a diagram illustrating a parity check matrix.

FIG. 76 is a diagram illustrating a parity check matrix.

FIG. 77 is a diagram illustrating a parity check matrix.

FIG. 78 is a diagram illustrating a parity check matrix.

FIG. 79 is a diagram illustrating a parity check matrix.

FIG. 80 is a diagram illustrating a parity check matrix.

FIG. 81 is a diagram illustrating a parity check matrix.

FIG. 82 is a diagram illustrating a parity check matrix.

FIG. 83 is a diagram illustrating an example of constellations when amodulation method is 16QAM.

FIG. 84 is a diagram illustrating an example of constellations when themodulation method is 64QAM.

FIG. 85 is a diagram illustrating an example of constellations when themodulation method is 256QAM.

FIG. 86 is a diagram illustrating an example of constellations when themodulation method is 1024QAM.

FIG. 87 is a diagram illustrating an example of the coordinates of asignal point of a UC when the modulation method is QPSK.

FIG. 88 is a diagram illustrating an example of the coordinates of asignal point of a 2D NUC when the modulation method is 16QAM.

FIG. 89 is a diagram illustrating an example of the coordinates of asignal point of a 2D NUC when the modulation method is 64QAM.

FIG. 90 is a diagram illustrating an example of the coordinates of asignal point of a 2D NUC when the modulation method is 256QAM.

FIG. 91 is a diagram illustrating an example of the coordinates of asignal point of a 1D NUC when the modulation method is 1024QAM.

FIG. 92 is a diagram illustrating the relationship between a symbol y,and a real part R_(e)(z_(q)) and an imaginary part Im(z_(q)) of acomplex number as the coordinates of a signal point z_(q) of a 1D NUCcorresponding to the symbol y.

FIG. 93 is a block diagram illustrating an example of the structure of ablock interleaver 25.

FIG. 94 is a diagram illustrating examples of the number of columns C ofparts 1 and 2 corresponding to a combination of a code length N and amodulation method and part column lengths R1 and R2.

FIG. 95 is a diagram illustrating block interleaving performed by theblock interleaver 25.

FIG. 96 is a diagram illustrating group-wise interleaving performed by agroup-wise interleaver 24.

FIG. 97 is a diagram illustrating a first example of a GW pattern for anLDPC code with a code length N of 64 kbits.

FIG. 98 is a diagram illustrating a second example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

FIG. 99 is a diagram illustrating a third example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

FIG. 100 is a diagram illustrating a fourth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

FIG. 101 is a diagram illustrating a fifth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

FIG. 102 is a diagram illustrating a sixth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

FIG. 103 is a diagram illustrating a seventh example of the GW patternfor the LDPC code with a code length N of 64 kbits.

FIG. 104 is a diagram illustrating an eighth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

FIG. 105 is a diagram illustrating a ninth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

FIG. 106 is a diagram illustrating a tenth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

FIG. 107 is a diagram illustrating an eleventh example of the GW patternfor the LDPC code with a code length N of 64 kbits.

FIG. 108 is a diagram illustrating a twelfth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

FIG. 109 is a diagram illustrating a thirteenth example of the GWpattern for the LDPC code with a code length N of 64 kbits.

FIG. 110 is a diagram illustrating a fourteenth example of the GWpattern for the LDPC code with a code length N of 64 kbits.

FIG. 111 is a diagram illustrating a fifteenth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

FIG. 112 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 113 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 114 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 115 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 116 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 117 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 118 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 119 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 120 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 121 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 122 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 123 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 124 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 125 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 126 is a diagram illustrating the results of a simulation formeasuring an error rate.

FIG. 127 is a block diagram illustrating an example of the structure ofa receiving device 12.

FIG. 128 is a block diagram illustrating an example of the structure ofa bit deinterleaver 165.

FIG. 129 is a flowchart describing an example of a process performed bya demapper 164, the bit deinterleaver 165, and an LDPC decoder 166.

FIG. 130 is a diagram illustrating an example of a parity check matrixof an LDPC code.

FIG. 131 is a diagram illustrating an example of a matrix (transformedparity check matrix) obtained by performing row permutation and columnpermutation for a parity check matrix.

FIG. 132 is a diagram illustrating an example of a transformed paritycheck matrix which is divided into 5×5 unit matrices.

FIG. 133 is a block diagram illustrating an example of the structure ofa decoding device which collectively performs P node operations.

FIG. 134 is a block diagram illustrating an example of the structure ofthe LDPC decoder 166.

FIG. 135 is a block diagram illustrating an example of the structure ofa block deinterleaver 54.

FIG. 136 is a block diagram illustrating another example of thestructure of the bit deinterleaver 165.

FIG. 137 is a block diagram illustrating a first example of thestructure of a receiving system to which the receiving device 12 can beapplied.

FIG. 138 is a block diagram illustrating a second example of thestructure of the receiving system to which the receiving device 12 canbe applied.

FIG. 139 is a block diagram illustrating a third example of thestructure of the receiving system to which the receiving device 12 canbe applied.

FIG. 140 is a block diagram illustrating an example of the structure ofan embodiment of a computer to which the present technology is applied.

MODE FOR CARRYING OUT THE INVENTION

Hereinafter, an LDPC code will be described before embodiments of thepresent technology are described.

<LDPC Code>

The LDPC code is a linear code and is not necessarily a binary code.However, here, it is assumed that the LDPC code is a binary code.

The maximum characteristic of the LDPC code is that a parity checkmatrix defining the LDPC code is sparse. Here, the sparse matrix means amatrix in which the number of “1s” which are elements of a matrix isvery small (a matrix in which most of the elements are 0).

FIG. 1 is a diagram illustrating an example of a parity check matrix Hof the LDPC code.

In the parity check matrix H illustrated in FIG. 1, the weight of eachcolumn (column weight) (the number of “1s”) is “3” and the weight ofeach row (row weight) is “6”.

In coding using the LDPC code (LDPC coding), for example, a generationmatrix G is generated on the basis of the parity check matrix H and thegeneration matrix G is multiplied by binary information bits to generatea code word (LDPC code).

Specifically, first, a coding device that performs the LDPC codingcalculates the generation matrix G in which a formula GH^(T)=0 isestablished between a transposed matrix H^(T) of the parity check matrixH and the generation matrix G. Here, when the generation matrix G is aK×N matrix, the coding device multiplies the generation matrix G by abit string (vector u) of information bits including K bits to generate acode word c (=uG) including N bits. The code word (LDPC code) generatedby the coding device is received by a receiver side through apredetermined communication path.

The LDPC code can be decoded by an algorithm that is calledprobabilistic decoding suggested by Gallager, that is, a message passingalgorithm using belief propagation on a so-called Tanner graph includinga variable node (also referred to as a message node) and a check node.Hereinafter, the variable node and the check node are appropriatelyreferred to as nodes simply.

FIG. 2 is a flowchart illustrating an LDPC code decoding process.

Hereinafter, a real value (a reception LLR) in which the likelihood of avalue “0” of an i-th code bit in the LDPC code (one code word) which isreceived by the receiver side is represented by a log likelihood ratiois appropriately referred to as a reception value u_(oi). In addition, amessage that is output from the check node is referred to as u_(j) and amessage that is output from the variable node is referred to as v_(i).

First, in the decoding of the LDPC code, as illustrated in FIG. 2, inStep S11, the LDPC code is received, the message (check node message)u_(j) is initialized to “0”, and a variable k which is an integer as acounter of a repetition process is initialized to “0”. Then, the processproceeds to Step S12. In Step S12, the message (variable node operation)v_(i) is calculated by performing an operation (variable node operation)represented by Formula (1) on the basis of the reception value u_(oi)obtained by receiving the LDPC code and the message u_(j) is calculatedby performing an operation (check node operation) represented by Formula(2) on the basis of the message v_(i).

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu} {Formula}\mspace{14mu} 1} \right\rbrack & \; \\{v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v} - 1}\; u_{j}}}} & (1) \\\left\lbrack {{Mathematical}\mspace{14mu} {Formula}\mspace{14mu} 2} \right\rbrack & \; \\{{\tanh \left( \frac{u_{j}}{2} \right)} = {\prod\limits_{i = 1}^{d_{c} - 1}\; {\tanh \left( \frac{v_{i}}{2} \right)}}} & (2)\end{matrix}$

Here, d_(v) and d_(c) in Formula (1) and Formula (2) are parameterswhich can be arbitrarily selected and indicate the number of “1s” in thelongitudinal direction (column) and the lateral direction (row) of theparity check matrix H, respectively. For example, in the case of an LDPCcode ((3, 6) LDPC code) with respect to the parity check matrix H inwhich the column weight is 3 and the row weight is 6 as illustrated inFIG. 1, d_(v) is 3 and d_(c) is 6.

In the variable node operation represented by Formula (1) and the checknode operation represented by Formula (2), since the message which isinput from an edge (a line connecting the variable node and the checknode) for outputting the message is not subjected to the operation, anoperation range is from 1 to d_(v)-1 or from 1 to d_(c)-1. In practice,the check node operation represented by Formula (2) is performed bymaking a table of a function R(v₁, v₂) that is represented by Formula(3) defined by two inputs v₁ and v₂ and one output and by continuously(recursively) using the table, as represented by Formula (4).

[Mathematical Formula 3]

x=2 tanh⁻¹{tanh(v ₁/2)tanh(v₂/2)}=R(v ₁ , v ₂)   (3)

[Mathematical Formula 4]

u _(j) =R(v ₁ , R(v ₂ , R(v ₃ , . . . R(v _(d) _(c) ₋₂ , v _(d) _(c)₋₁))))   (4)

In Step S12, the variable k is incremented by “1” and the processproceeds to Step S13. In Step S13, it is determined whether the variablek is greater than a predetermined number of repetitive decodingoperations C. When it is determined in Step S13 that the variable k isnot greater than C, the process returns to Step S12 and the same processas described above is repeated.

When it is determined in Step S13 that the variable k is greater than C,the process proceeds to Step S14. An operation represented by Formula(5) is performed to calculate the message v_(i) as the decoding resultthat is finally output and the message v_(i) is output. The LDPC codedecoding process ends.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu} {Formula}\mspace{14mu} 5} \right\rbrack & \; \\{v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v}}\; u_{j}}}} & (5)\end{matrix}$

Here, the operation represented by Formula (5) is different from thevariable node operation represented by Formula (1) and is performedusing the messages u_(j) from all of the edges connected to the variablenode.

FIG. 3 is a diagram illustrating an example of the parity check matrix Hof the (3, 6) LDPC code (a coding rate of 1/2 and a code length of 12).

In the parity check matrix H illustrated in FIG. 3, similarly to FIG. 1,the weight of a column is 3 and the weight of a row is 6.

FIG. 4 is a diagram illustrating a Tanner graph of the parity checkmatrix H illustrated in FIG. 3.

Here, in FIG. 4, the check node is represented by “+” (plus) and thevariable node is represented by “=” (equal). The check node and thevariable node correspond to a row and a column of the parity checkmatrix H, respectively. A line that connects the check node and thevariable node is the edge and corresponds to an element “1” of theparity check matrix.

That is, in FIG. 4, when an element in a j-th row and an i-th column ofthe parity check matrix is 1, an i-th variable node (node represented by“=”) from the upper side and a j-th check node (node represented by “+”)from the upper side are connected by the edge. The edge indicates that acode bit corresponding to the variable node has a restriction conditioncorresponding to the check node.

In a sum product algorithm that is an LDPC code decoding method, thevariable node operation and the check node operation are repetitivelyperformed.

FIG. 5 is a diagram illustrating the variable node operation performedin the variable node.

In the variable node, the message v_(i) that corresponds to the edge tobe calculated is calculated by the variable node operation representedby Formula (1), using messages u₁ and u₂ from the remaining edgesconnected to the variable node and the reception value u_(oi). Themessages that correspond to the other edges are calculated by the samemethod as described above.

FIG. 6 is a diagram illustrating the check node operation performed inthe check node.

Here, the check node operation represented by Formula (2) can berewritten by Formula (6) using the relationship of the followingformula: a×b=exp{ln(|a|)+ln(|b|)}×sign(a)×sign(b). However, sign(x) is 1when x≥0 is satisfied and is −1 when x<0 is satisfied.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu} {Formula}\mspace{14mu} 6} \right\rbrack & \; \\\begin{matrix}{u_{j} = {2{\tanh^{- 1}\left( {\prod\limits_{i = 1}^{d_{c} - 1}{\tanh \left( \frac{v_{i}}{2} \right)}} \right)}}} \\{= {2{\tanh^{- 1}\left\lbrack {\exp \left\{ {\sum\limits_{i = 1}^{d_{c} - 1}{\ln \left( {{\tanh \left( \frac{v_{i}}{2} \right)}} \right)}} \right\} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( {\tanh \left( \frac{v_{i}}{2} \right)} \right)}}} \right\rbrack}}} \\{= {2{\tanh^{- 1}\left\lbrack {\exp \left\{ {- \left( {\sum\limits_{i = 1}^{d_{c} - 1}{- {\ln \left( {\tanh \left( \frac{v_{i}}{2} \right)} \right)}}} \right)} \right\}} \right\rbrack} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( v_{i} \right)}}}}\end{matrix} & (6)\end{matrix}$

When a function ϕ(x) is defined as a formula ϕ(x)=ln(tanh(x/2)) at x≥0,a formula ϕ⁻¹(x)=2 tanh⁻¹(e^(−x)) is established. Therefore, Formula (6)can be changed to Formula (7).

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu} {Formula}\mspace{14mu} 7} \right\rbrack & \; \\{u_{j} = {{\varphi^{- 1}\left( {\sum\limits_{i = 1}^{d_{c} - 1}{\varphi \left( {v_{i}} \right)}} \right)} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( v_{i} \right)}}}} & (7)\end{matrix}$

In the check node, the check node operation represented by Formula (2)is performed according to Formula (7).

That is, in the check node, as illustrated in FIG. 6, the message u_(j)corresponding to the edge to be calculated is calculated by the checknode operation represented by Formula (7), using messages v₁, v₂, v₃,v₄, and v₅ from the remaining edges connected to the check node. Themessages that correspond to the other edges are calculated by the samemethod as described above.

The function ϕ(x) in Formula (7) can be represented by a formulaϕ(x)=ln((e^(x)+1)/(e^(x)−1)) and ϕ(x)=ϕ⁻¹(x) is established when x>0 issatisfied. When the functions ϕ(x) and ϕ⁻¹(x) are provided in hardware,in some cases, they are provided using a lookup table (LUT). Both thefunctions become the same LUT.

<Example of Structure of Transmission System to Which the PresentInvention is Applied>

FIG. 7 is a diagram illustrating an example of the structure of anembodiment of a transmission system (a system means a logical group of aplurality of devices and it does not matter whether devices having eachstructure are provided in the same housing) to which the presenttechnology is applied.

In FIG. 7, the transmission system includes a transmitting device 11 anda receiving device 12.

For example, the transmitting device 11 transmits (broadcasts) (sends) atelevision program. That is, for example, the transmitting device 11encodes target data to be transmitted, such as image data and audio dataas a program, into LDPC codes, and transmits the LDPC codes through acommunication path 13, such as a satellite channel, a terrestrialchannel, or a cable (wired line). The receiving device 12 receives theLDPC codes transmitted from the transmitting device 11 through thecommunication path 13, decodes the LDPC codes into target data, andoutputs the target data.

Here, it has been known that the LDPC code used by the transmissionsystem illustrated in FIG. 7 has very high capability in an additivewhite Gaussian noise (AWGN) communication path.

In the communication path 13, in some cases, a burst error or erasureoccurs. For example, in particular, when the communication path 13 is aterrestrial channel, in some cases, the power of a specific symbol is 0(erasure) according to the delay of an echo (a channel other than a mainchannel) in a multi-path environment in which a desired-to-undesiredratio (D/U) is 0 dB (the power of Undesired=echo is equal to the powerof Desired=main path) in an orthogonal frequency division multiplexing(OFDM) system.

In a flutter (a communication path in which delay is 0 and to which anecho having a Doppler frequency is added), in some cases, when D/U is 0dB, the power of all of the OFDM symbols at a specific time is 0(erasure) according to the Doppler frequency.

In addition, in some cases, a burst error occurs due to the conditionsof a wiring line from a receiving unit (not illustrated), such as anantenna that receives signals from the transmitting device 11, on theside of the receiving device 12 to the receiving device 12 or theinstability of a power supply of the receiving device 12.

In the decoding of the LDPC code, in the variable node corresponding tothe column of the parity check matrix H and the code bit of the LDPCcode, as illustrated in FIG. 5, the variable node operation representedby Formula (1) involving the addition of (the reception value u_(oi) of)the code bit of the LDPC code is performed. Therefore, when an erroroccurs in the code bits used for the variable node operation, theaccuracy of the calculated message is reduced.

In the decoding of the LDPC code, in the check node, the check nodeoperation represented by Formula (7) is performed, using the messagecalculated in the variable node connected to the check node. Therefore,when the number of check nodes to which (the code bits of the LDPC codescorresponding to) a plurality of variable nodes, in which errors(including erasure) simultaneously occur, are connected increases, adecoding performance deteriorates.

That is, for example, when erasure simultaneously occurs in two or moreof the variable nodes connected to the check node, the check nodereturns a message in which the probability of a value being 0 and theprobability of a value being 1 are equal to each other to all of thevariable nodes. In this case, the check node that returns the message ofthe equal probability does not contribute to one decoding process (oneset of the variable node operation and the check node operation). As aresult, it is necessary to increase the number of times the decodingprocess is repeated and the decoding performance deteriorates. Inaddition, the power consumption of the receiving device 12 that decodesthe LDPC code increases.

Therefore, in the transmission system illustrated in FIG. 7, it ispossible to improve tolerance to a burst error or erasure whilemaintaining the performance in the AWGN communication path (AWGNchannel).

<Example of Structure of Transmitting Device 11>

FIG. 8 is a block diagram illustrating an example of the structure ofthe transmitting device 11 illustrated in FIG. 7.

In the transmitting device 11, one or more input streams are supplied astarget data to a mode adaptation/multiplexer 111.

The mode adaptation/multiplexer 111 performs, for example, a modeselection process and a process of multiplexing one or more inputstreams supplied thereto, if necessary, and supplies the processed datato a padder 112.

The padder 112 performs necessary zero padding (insertion of Null) forthe data from the mode adaptation/multiplexer 111 and supplies dataobtained by the zero padding to a BB scrambler 113.

The BB scrambler 113 performs base-band scrambling (BB scrambling) forthe data from the padder 112 and supplies data obtained by the BBscrambling to a BCH encoder 114.

The BCH encoder 114 performs BCH coding for the data from the BBscrambler 113 and supplies data obtained by the BCH coding as LDPCtarget data to be subjected to LDPC coding to an LDPC encoder 115.

The LDPC encoder 115 performs LDPC coding for the LDPC target datasupplied from the BCH encoder 114 according to a parity check matrix inwhich a parity matrix that is a portion corresponding to the parity bitsof the LDPC code has a dual diagonal structure and outputs an LDPC codehaving the LDPC target data as information bits.

That is, the LDPC encoder 115 performs LDPC coding (corresponding to theparity check matrix) which is defined by a predetermined standard, suchas DVB-S.2, DVB-T.2, or DVB-C.2, or LDPC coding (corresponding to theparity check matrix) which is scheduled to be used in ATSC3.0 for theLDPC target data and outputs the LDPC code obtained by the LDPC coding.

Here, the LDPC code defined by the DVB-T.2 standard or the LDPC codewhich is scheduled to be used in ATSC3.0 is an irregular repeataccumulate (IRA) code and a parity matrix of the parity check matrix ofthe LDPC code has a dual diagonal structure. The parity matrix and thedual diagonal structure will be described below. The IRA code isdescribed in, for example, “Irregular Repeat-Accumulate Codes”, H. Jin,A. Khandekar, and R. J. McEliece, in Proceedings of 2nd InternationalSymposium on Turbo codes and Related Topics, pp. 1-8, Sept. 2000.

The LDPC code output from the LDPC encoder 115 is supplied to a bitinterleaver 116.

The bit interleaver 116 performs bit interleaving, which will bedescribed below, for the LDPC code supplied from the LDPC encoder 115and supplies the bit-interleaved LDPC code to a mapper 117.

The mapper 117 maps the LDPC code supplied from the bit interleaver 116to a signal point indicating one symbol of quadrature modulation inunits (symbol unit) of one or more code bits of the LDPC code to performquadrature modulation (multilevel modulation).

That is, the mapper 117 performs quadrature modulation by mapping theLDPC code supplied from the bit interleaver 116 to a signal point whichis determined by a modulation method for performing quadraturemodulation for the LDPC code in an IQ plane (IQ constellation) definedby an I-axis indicating an I component that has the same phase as acarrier wave and a Q-axis indicating a Q component that is orthogonal tothe carrier wave.

When the number of signal points determined by the quadrature modulationmethod performed by the mapper 117 is 2^(m), the code bits of m bits ofthe LDPC code are used as a symbol (one symbol) and the mapper 117 mapsthe LDPC code supplied from the bit interleaver 116 to a signal pointindicating the symbol among 2^(m) signal points in units of symbols.

Here, as the quadrature modulation method performed by the mapper 117,for example, there are the following modulation methods: modulationmethods defined by the DVB-T.2 standard; modulation methods scheduled tobe used in ATSC3.0; and other modulation methods, such as binary phaseshift keying (BPSK), quadrature phase shift keying (QPSK), 8 phase-shiftkeying (8PSK), 16 amplitude phase-shift keying (16APSK), 32APSK, 16quadrature amplitude modulation (16QAM), 16QAM, 64QAM, 256QAM, 1024QAM,4096QAM, and 4 pulse amplitude modulation (4PAM). For example, theoperator of the transmitting device 11 presets which modulation methodis used for quadrature modulation in the mapper 117.

Data (the result of mapping the symbol to the signal point) obtained bythe process of the mapper 117 is supplied to a time interleaver 118.

The time interleaver 118 performs time interleaving (interleaving in atime direction) for the data supplied from the mapper 117 in units ofsymbols and supplies data obtained by the time interleaving to a singleinput-single output/multiple input-single output (SISO/MISO) encoder119.

The SISO/MISO encoder 119 performs spatiotemporal coding for the datasupplied from the time interleaver 118 and supplies the data to afrequency interleaver 120.

The frequency interleaver 120 performs frequency interleaving(interleaving in a frequency direction) for the data supplied from theSISO/MISO encoder 119 in units of symbols and supplies the data to aframe builder/resource allocation unit 131.

For example, control data (signalling) for transmission control, such asbase band signalling (BB signalling) (BB header), is supplied to a BCHencoder 121.

The BCH encoder 121 performs BCH coding for the control data suppliedthereto, similarly to the BCH encoder 114, and supplies data obtained bythe BCH coding to an LDPC encoder 122.

The LDPC encoder 122 performs LDPC coding for the data from the BCHencoder 121 as LDPC target data, similarly to the LDPC encoder 115, andoutputs an LDPC code obtained by the LDPC coding to a mapper 123.

Similarly to the mapper 117, the mapper 123 performs quadraturemodulation by mapping the LDPC code supplied from the LDPC encoder 122to a signal point indicating one symbol of quadrature modulation in unit(symbol unit) of one or more code bits of the LDPC code and suppliesdata obtained by the quadrature modulation to a frequency interleaver124.

Similarly to the frequency interleaver 120, the frequency interleaver124 performs frequency interleaving for the data supplied from themapper 123 in units of symbols and supplies the data to the framebuilder/resource allocation unit 131.

The frame builder/resource allocation unit 131 inserts symbols of pilotsinto necessary positions of the data (symbols) supplied from thefrequency interleavers 120 and 124, forms a frame (for example, aphysical layer (PL) frame, a T2 frame, or a C2 frame) including apredetermined number of symbols from the resultant data (symbols), andsupplies the frame to an OFDM generation unit 132.

The OFDM generation unit 132 generates an OFDM signal, whichcorresponding to the frame supplied from the frame builder/resourceallocation unit 131, from the frame and transmits the OFDM signalthrough the communication path 13 (FIG. 7).

For example, the transmitting device 11 may be configured, withoutincluding some of the blocks illustrated in FIG. 8, such as the timeinterleaver 118, the SISO/MISO encoder 119, the frequency interleaver120 and the frequency interleaver 124.

<Example of Structure of Bit Interleaver 116>

FIG. 9 is a block diagram illustrating an example of the structure ofthe bit interleaver 116 illustrated in FIG. 8.

The bit interleaver 116 has a function of interleaving data and includesa parity interleaver 23, a group-wise interleaver 24, and a blockinterleaver 25.

The parity interleaver 23 performs parity interleaving for interleavingthe parity bits of the LDPC code supplied from the LDPC encoder 115 intothe positions of other parity bits and supplies the LDPC code subjectedto the parity interleaving to the group-wise interleaver 24.

The group-wise interleaver 24 performs group-wise interleaving for theLDPC code from the parity interleaver 23 and supplies the LDPC codesubjected to the group-wise interleaving to the block interleaver 25.

Here, in the group-wise interleaving, an LDPC code corresponding to onecode is divided into sections each having 360 bits equal to a unit sizeP, which will be described below, from the head and 360 bits in eachsection form a bit group. The LDPC code from the parity interleaver 23is interleaved in units of bit groups.

When group-wise interleaving is performed, an error rate can be reduced,as compared to a case in which group-wise interleaving is not performed.As a result, it is possible to ensure high communication quality in datatransmission.

The block interleaver 25 performs block interleaving for inverselymultiplexing the LDPC code from the group-wise interleaver 24 to changethe LDPC code corresponding to one code, for example, to an m-bit symbolthat is the unit of mapping, and supplies the symbol to the mapper 117(FIG. 8).

Here, in the block interleaving, for example, in a storage region inwhich columns that correspond to the number of bits m of the symbol andserve as storage regions for storing a predetermined number of bits inthe column (longitudinal) direction are arranged in the row (lateral)direction, the LDPC code from the group-wise interleaver 24 is writtenin the column direction and is read in the row direction. In this way,the LDPC code corresponding to one code is changed to an m-bit symbol.

<Parity Check Matrix of LDPC Code>

FIG. 10 is a diagram illustrating an example of the parity check matrixH that is used for LDPC coding by the LDPC encoder 115 illustrated inFIG. 8.

The parity check matrix H has a low-density generation matrix (LDGM)structure and can be represented by a formula H=[H_(A)|H_(T)] (a matrixin which elements of an information matrix H_(A) are left elements andelements of a parity matrix H_(T) are right elements) using theinformation matrix H_(A) corresponding to information bits and theparity matrix H_(T) corresponding to parity bits among the code bits ofthe LDPC code.

Here, the number of information bits and the number of parity bits amongthe code bits of one LDPC code (one code word) are referred to as aninformation length K and a parity length M, respectively, and the numberof code bits of one LDPC code (one code word) is referred to as a codelength N (=K+M).

The information length K and the parity length M in the LDPC code havinga certain code length N are determined by a coding rate. The paritycheck matrix H is an M×N matrix (a matrix of M rows and N columns). Theinformation matrix H_(A) is an M×K matrix and the parity matrix H_(T) isan M×M matrix.

FIG. 11 is a diagram illustrating an example of the parity matrix H_(T)of the parity check matrix H that is used for LDPC coding by the LDPCencoder 115 illustrated in FIG. 8.

The parity matrix H_(T) of the parity check matrix H that is used forLDPC coding by the LDPC encoder 115 is the same as the parity matrixH_(T) of the parity check matrix H of the LDPC code which is defined by,for example, the DVB-T.2 standard.

The parity matrix H_(T) of the parity check matrix H of the LDPC codewhich is defined by, for example, the DVB-T.2 standard is a lowerbidiagonal matrix in which elements “1” are arranged in a staircaseshape, as illustrated in FIG. 11. In parity matrix H_(T), the weight ofa first row is 1 and the weight of the remaining rows is 2. The weightof the final column is 1 and the weight of the remaining columns is 2.

As described above, the LDPC code of the parity check matrix H in whichthe parity matrix H_(T) has the lower bidiagonal structure can be easilygenerated using the parity check matrix H.

That is, the LDPC code (one code word) is represented by a row vector cand a column vector obtained by transposing the row vector isrepresented by c^(T). In addition, in the row vector c which is the LDPCcode, the information bits are represented by a row vector A and theparity bits is represented by a row vector T.

In this case, the row vector c can be represented by a formula c=[A|T](a row vector in which elements of the row vector A are left elementsand elements of the row vector T are right elements) using the rowvector A as the information bits and the row vector T as the paritybits.

The parity check matrix H and the row vector c=[A|T] as the LDPC codeneed to satisfy a formula Hc^(T)=0. When the parity matrix H_(T) of theparity check matrix H=[H_(A)|H_(T)] has the dual diagonal structureillustrated in FIG. 11, the row vector T that corresponds to the paritybits forming the row vector c=[A|T] satisfying the formula Hc^(T)=0 canbe sequentially (in order) calculated by sequentially setting elementsin each row to 0 from elements in a first row of the column vectorHc^(T) in the formula Hc^(T)=0.

FIG. 12 is a diagram illustrating the parity check matrix H of the LDPCcode which is defined by, for example, the DVB-T.2 standard.

The weight of a KX column from the first column of the parity checkmatrix H of the LDPC code which is defined by, for example, the DVB-T.2standard is X. The weight of a K3 column is 3. The weight of an (M−1)column is 2. The weight of the final column is 1.

Here, KX+K3+M−1+1 is equal to the code length N.

FIG. 13 is a diagram illustrating column numbers KX, K3, and M and acolumn weight X with respect to each coding rate r of the LDPC codewhich is defined by the DVB-T.2 standard.

For example, in the DVB-T.2 standard, LDPC codes with a code length N of64800 bits and a code length N of 16200 bits are defined.

For the LDPC code with a code length N of 64800 bits, 11 coding rates(nominal rates) of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and9/10 are defined.

In the LDPC code with a code length N of 16200 bits, 10 coding rates of1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9 are defined.

Hereinafter, a code length N of 64800 bits is referred to as 64 kbitsand a code length N of 16200 bits is referred to as 16 kbits.

For the LDPC code, an error rate tends to be lower in a code bitcorresponding to a column with a larger column weight in the paritycheck matrix H.

In the parity check matrix H that is illustrated in FIGS. 12 and 13 andis defined by, for example, the DVB-T.2 standard, a column which iscloser to the head side (left side) tends to have a larger weight.Therefore, in the LDPC code corresponding to the parity check matrix H,a code bit that is closer to the head side tends to have higher errortolerance (higher tolerance to errors) and a code bit that is closer tothe end tends to have lower tolerance to errors.

<Parity Interleaving>

The parity interleaving performed by the parity interleaver 23illustrated in FIG. 9 will be described with reference to FIGS. 14 to16.

FIG. 14 is a diagram illustrating an example of (a part of) a Tannergraph of the parity check matrix of the LDPC code.

As illustrated in FIG. 14, when an error, such as erasure,simultaneously occurs in a plurality of variable nodes, for example, twovariable nodes among (the code bits corresponding to) the variable nodesconnected to the check node, the check node returns a message, in whichthe probability of a value being 0 and the probability of a value being1 are equal to each other, to all of the variable nodes connected to thecheck node. Therefore, when erasure simultaneously occurs in a pluralityof variable nodes connected to the same check node, a decodingperformance deteriorates.

However, similarly to the LDPC code which is defined by, for example,the DVB-T.2 standard, the LDPC code that is output from the LDPC encoder115 illustrated in FIG. 8 is an IRA code and the parity matrix H_(T) ofthe parity check matrix H has a dual diagonal structure, as illustratedin FIG. 11.

FIG. 15 is a diagram illustrating an example of the parity matrix H_(T)having a dual diagonal structure and a Tanner graph corresponding to theparity matrix H_(T), as illustrated in FIG. 11.

A of FIG. 15 illustrates an example of the parity matrix H_(T) having adual diagonal structure and B of FIG. 15 illustrates the Tanner graphcorresponding to the parity matrix H_(T) illustrated in A of FIG. 15.

In the parity matrix H_(T) with a dual diagonal structure, elements “1”are adjacent to each other in each row (except for the first row).Therefore, in the Tanner graph of the parity matrix H_(T), two adjacentvariable nodes corresponding to a column of two adjacent elements inwhich the value of the parity matrix H_(T) is 1 are connected to thesame check node.

Therefore, when parity bits corresponding to the two adjacent variablenodes indicate an error at the same time due to, for example, a bursterror and erasure, the check node that is connected to two variablenodes (variable nodes requiring a message using parity bits)corresponding to the two parity bits indicating the error returns amessage, in which the probability of a value being 0 and the probabilityof a value being 1 are equal to each other, to the variable nodesconnected to the check node. As a result, the decoding performancedeteriorates. Furthermore, when the burst length (the number ofconsecutive parity bits indicating an error) is large, the number ofcheck nodes that return the message indicating equal probabilityincreases and the decoding performance further deteriorates.

Therefore, the parity interleaver 23 (FIG. 9) performs parityinterleaving for interleaving the parity bits of the LDPC code suppliedfrom the LDPC encoder 115 into the positions of other parity bits, inorder to prevent deterioration of the decoding performance.

FIG. 16 is a diagram illustrating the parity matrix H_(T) of the paritycheck matrix H corresponding to the LDPC code that has been subjected toparity interleaving by the parity interleaver 23 illustrated in FIG. 9.

Here, the information matrix H_(A) of the parity check matrix Hcorresponding to the LDPC code that is output from the LDPC encoder 115has a cyclic structure, similarly to the information matrix of theparity check matrix H corresponding to the LDPC code which is definedby, for example, the DVB-T.2 standard.

The cyclic structure means a structure in which a certain column ismatched with a column obtained by cyclically shifting another column.For example, the cyclic structure includes a structure in which theposition of 1 in each row of P columns becomes a position obtained bycyclically shifting the first column of the P columns in the columndirection by a predetermined value, such as a value that is proportionalto a value q obtained by dividing a parity length M, for every Pcolumns. Hereinafter, the P columns in the cyclic structure areappropriately referred to as a unit size.

As the LDPC code that is defined by, for example, the DVB-T.2 standard,as described in FIG. 12 and FIG. 13, there are two kinds of LDPC codes,that is, an LDPC code with a code length N of 64800 bits and an LDPCcode with a code length N of 16200 bits. For both the two kinds of LDPCcodes, the unit size P is defined as 360 which is one of the divisors ofthe parity length M except for 1 and M.

The parity length M is a value other than prime numbers representedbyaformula M=q×P=q×360, using a value q that varies depending on thecoding rate. Therefore, similarly to the unit size P, the value q isanother one of the divisors of the parity length M except for 1 and Mand is obtained by dividing the parity length M by the unit size P (theproduct of P and q, which are the divisors of the parity length M, isthe parity length M).

As described above, when an information length is K, an integer that isequal to or greater than 0 and less than P is x, and an integer that isequal to or greater than 0 and less than q is y, the parity interleaver23 parity interleaving for interleaving a (K+qx+y+1)-th code bit amongthe code bits of an LDPC code of N bits into the position of a(K+Py+x+1)-th code bit.

Since both the (K+qx+y+1)-th code bit and the (K+Py+x+1)-th code bit arecode bits after a (K+1)-th code bit, they are parity bits. Therefore,the position of the parity bits of the LDPC code is moved by the parityinterleaving.

According to the parity interleaving, (the parity bits corresponding to)the variable nodes connected to the same check node are separated by theunit size P, that is, 360 bits in this example. Therefore, when theburst length is less than 360 bits, it is possible to prevent errorsfrom occurring in a plurality of variable nodes connected to the samecheck node at the same time. As a result, it is possible to improvetolerance to the burst error.

The LDPC code after the parity interleaving for interleaving the(K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bitis matched with an LDPC code having a parity check matrix (hereinafter,referred to as a transformed parity check matrix) obtained by performingcolumn permutation for substituting the (K+qx+y+1)-th column of theoriginal parity check matrix H with the (K+Py+x+1)-th column.

As illustrated in FIG. 16, a parity matrix of the transformed paritycheck matrix has a pseudo-cyclic structure that uses the P columns (360columns in FIG. 16) as a unit.

Here, the pseudo-cyclic structure means a structure in which a part of amatrix is not cyclic.

The transformed parity check matrix that is obtained by performingcolumn permutation corresponding to parity interleaving for the paritycheck matrix of the LDPC code which is defined by, for example, theDVB-T.2 standard does not have the (perfect) cyclic structure, but hasthe pseudo-cyclic structure since the number of elements “1” is oneshort (an element “0” is present) in a 360×360 matrix at the upper rightcorner (a shifted matrix which will be described below) of thetransformed parity check matrix.

The transformed parity check matrix of the parity check matrix of theLDPC code that is output from the LDPC encoder 115 has a pseudo-cyclicstructure, similarly to the transformed parity check matrix of theparity check matrix of the LDPC code that is defined, for example, bythe DVB-T.2 standard.

The transformed parity check matrix illustrated in FIG. 16 is a matrixthat is obtained by performing the permutation of rows (rowpermutation), in addition to column permutation corresponding to theparity interleaving, for the original parity check matrix H such thatthe transformed parity check matrix is a constitutive matrix, which willbe described below.

FIG. 17 is a flowchart illustrating the process performed by the LDPCencoder 115, the bit interleaver 116, and the mapper 117 illustrated inFIG. 8.

The LDPC encoder 115 waits for the supply of the LDPC target data fromthe BCH encoder 114. In Step S101, the LDPC encoder 115 encodes the LDPCtarget data into the LDPC code and supplies the LDPC code to the bitinterleaver 116. Then, the process proceeds to Step S102.

In Step S102, the bit interleaver 116 performs bit interleaving for theLDPC code supplied from the LDPC encoder 115 and supplies a symbolobtained by the bit interleaving to the mapper 117. The process proceedsto Step S103.

That is, in Step S102, in the bit interleaver 116 (FIG. 9), the parityinterleaver 23 performs parity interleaving for the LDPC code suppliedfrom the LDPC encoder 115 and supplies the LDPC code subjected to theparity interleaving to the group-wise interleaver 24.

The group-wise interleaver 24 performs group-wise interleaving for theLDPC code supplied from the parity interleaver 23 and supplies the LDPCcode to the block interleaver 25.

The block interleaver 25 performs block interleaving for the LDPC codesubjected to the group-wise interleaving by the group-wise interleaver24 and supplies an m-bit symbol obtained by the block interleaving tothe mapper 117.

In Step S103, the mapper 117 maps the symbol supplied from the blockinterleaver 25 to any one of 2^(m) signal points which are determined bythe quadrature modulation method performed by the mapper 117 to performquadrature modulation, and supplies data obtained by the quadraturemodulation to the time interleaver 118.

As described above, the parity interleaving or the group-wiseinterleaving makes it possible to improve an error rate when a pluralityof code bits of the LDPC code are transmitted as one symbol.

In FIG. 9, for convenience of explanation, the parity interleaver 23,which is a block for performing parity interleaving, and the group-wiseinterleaver 24, which is a block for performing group-wise interleaving,are individually provided. However, the parity interleaver 23 and thegroup-wise interleaver 24 may be integrally provided.

That is, both the parity interleaving and the group-wise interleavingcan be performed by writing and reading code bits to and from the memoryand can be represented by a matrix which converts an address (writeaddress) for writing code bits into an address (read address) forreading code bits.

Therefore, when a matrix obtained by multiplying a matrix indicatingparity interleaving by a matrix indicating group-wise interleaving iscalculated, code bits are converted by the matrix and parityinterleaving is performed. In addition, group-wise interleaving isperformed for the LDPC code subjected to the parity interleaving. Inthis way, it is possible to obtain the result of the group-wiseinterleaving.

In addition, the parity interleaver 23, the group-wise interleaver 24,and the block interleaver 25 may be integrally provided.

That is, the block interleaving performed by the block interleaver 25can be represented by a matrix which converts a write address of thememory storing the LDPC code into a read address.

Therefore, when a matrix obtained by multiplying a matrix indicatingparity interleaving, a matrix indicating group-wise interleaving, and amatrix indicating block interleaving is calculated, the parityinterleaving, the group-wise interleaving, and the block interleavingcan be collectively performed by the matrix.

<Example of Structure of LDPC Encoder 115>

FIG. 18 is a block diagram illustrating an example of the structure ofthe LDPC encoder 115 illustrated in FIG. 8.

The LDPC encoder 122 illustrated in FIG. 8 has the same structure as theLDPC encoder 115.

As described in FIG. 12 and FIG. 13, for example, in the DVB-T.2standard, two types of LDPC codes having a code length N of 64800 bitsand a code length N of 16200 bits are defined.

For the LDPC code with a code length N of 64800 bits, 11 coding rates of1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and 9/10 are defined.For the LDPC code with a code length N of 16200 bits, 10 coding rates of1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9 are defined (FIG.12 and FIG. 13).

For example, the LDPC encoder 115 can perform coding (error correctioncoding) for the LDPC code having a code length N of 64800 bits or 16200bits at each coding rate, according to the parity check matrix H whichis prepared for each code length N and each coding rate.

The LDPC encoder 115 includes a coding processing unit 601 and a storageunit 602.

The coding processing unit 601 includes a coding rate setting unit 611,an initial value table reading unit 612, a parity check matrixgeneration unit 613, an information bit reading unit 614, a codingparity calculation unit 615, and a control unit 616, performs LDPCcoding for the LDPC target data supplied from the LDPC encoder 115, andsupplies an LDPC code obtained by the LDPC coding to the bit interleaver116 (FIG. 8).

That is, the coding rate setting unit 611 sets the code length N and thecoding rate of the LDPC code, according to, for example, an operation ofthe operator.

The initial value table reading unit 612 reads a parity check matrixinitial value table, which corresponds to the code length N and thecoding rate set by the coding rate setting unit 611 and will bedescribed below, from the storage unit 602.

The parity check matrix generation unit 613 arranges elements “1” of aninformation matrix H_(A) corresponding to the information length K (=thecode length N−the parity length M) which corresponds to the code lengthN and the coding rate set by the coding rate setting unit 611 in thecolumn direction in a cycle of 360 columns (unit size P) to generate aparity check matrix H, on the basis of the parity check matrix initialvalue table read by the initial value table reading unit 612, and storesthe parity check matrix H in the storage unit 602.

The information bit reading unit 614 reads (extracts) information bitscorresponding to the information length K from the LDPC target datasupplied to the LDPC encoder 115.

The coding parity calculation unit 615 reads the parity check matrix Hgenerated by the parity check matrix generation unit 613 from thestorage unit 602, calculates parity bits for the information bits readby the information bit reading unit 614, on the basis of a predeterminedformula, using the parity check matrix H, and generates a code word(LDPC code).

The control unit 616 controls each of the blocks forming the codingprocessing unit 601.

For example, a plurality of parity check matrix initial value tablesthat correspond to the plurality of coding rates illustrated in FIGS. 12and 13 for each code length N of 64800 bits or 16200 bits are stored inthe storage unit 602. In addition, the storage unit 602 temporarilystores data that is required for the process of the coding processingunit 601.

FIG. 19 is a flowchart illustrating an example of the process of theLDPC encoder 115 illustrated in FIG. 18.

In Step S201, the coding rate setting unit 611 determines (sets) thecode length N and the coding rate r for LDPC coding.

In Step S202, the initial value table reading unit 612 reads apredetermined parity check matrix initial value table corresponding tothe code length N and the coding rate r determined by the coding ratesetting unit 611 from the storage unit 602.

In Step S203, the parity check matrix generation unit 613 calculates(generates) the parity check matrix H of the LDPC code having the codelength N and the coding rate r determined by the coding rate settingunit 611, using the parity check matrix initial value table that is readfrom the storage unit 602 by the initial value table reading unit 612,and supplies the parity check matrix H to the storage unit 602. Theparity check matrix H is stored in the storage unit 602.

In Step S204, the information bit reading unit 614 reads the informationbits with the information length K (=N×r) corresponding to the codelength N and the coding rate r determined by the coding rate settingunit 611 from the LDPC target data supplied to the LDPC encoder 115,reads the parity check matrix H calculated by the parity check matrixgeneration unit 613 from the storage unit 602, and supplies theinformation bits and the parity check matrix H to the coding paritycalculation unit 615.

In Step S205, the coding parity calculation unit 615 sequentiallycalculates the parity bits of a code word c satisfying the followingFormula (8), using the information bits and the parity check matrix Hfrom the information bit reading unit 614.

Hc^(T)=0   (8)

In Formula (8), c indicates a row vector as a code word (LDPC code) andc^(T) indicates the transposition of the row vector c.

As described above, when the information bits of the row vector c as theLDPC code (one code word) are represented by a row vector A and theparity bits thereof are represented by a row vector T, the row vector ccan be represented by a formula c=[A/T] using the row vector A as theinformation bits and the row vector T as the parity bits.

The parity check matrix H and the row vector c=[A|T] as the LDPC codeneed to satisfy the formula Hc^(T)=0. When the parity matrix H_(T) ofthe parity check matrix H=[H_(A)|H_(T)] has the dual diagonal structureillustrated in FIG. 11, the row vector T that corresponds to the paritybits forming the row vector c=[A|T] satisfying the formula Hc^(T)=0 canbe sequentially calculated by sequentially setting elements in each rowto 0 from elements in the first row of the column vector Hc^(T) in theformula Hc^(T)=0.

The coding parity calculation unit 615 calculates the parity bits T withrespect to the information bits A from the information bit reading unit614 and outputs the code word c=[A/T] represented by the informationbits A and the parity bits T as the LDPC coding result of theinformation bits A.

Then, in Step S206, the control unit 616 determines whether the LDPCcoding ends. When it is determined in Step S206 that the LDPC codingdoes not end, that is, when LDPC target data to be subjected to the LDPCcoding remains, the process returns to Step S201 (or Step S204). Then,the process from Step S201 (or Step S204) to Step S206 is repeated.

When it is determined in Step S206 that the LDPC coding ends, that is,when the LDPC target data to be subjected to the LDPC coding does notremain, the LDPC encoder 115 ends the process.

As described above, the parity check matrix initial value tablescorresponding to each code length N and each coding rate r are preparedand the LDPC encoder 115 performs LDPC coding for an LDPC code with apredetermined code length N and a predetermined coding rate r, using theparity check matrix H that is generated from the parity check matrixinitial value table corresponding to the predetermined code length N andthe predetermined coding rate r.

<Example of Parity Check Matrix Initial Value Table>

The parity check matrix initial value table is a table that indicatesthe positions of elements “1” of the information matrix H_(A) (FIG. 10),which corresponds to the information length K corresponding to the codelength N and the coding rate r of the LDPC code (the LDPC code definedby the parity check matrix H), in the parity check matrix H for every360 columns (unit size P) and is created for each parity check matrix Hwith each code length N and each coding rate r in advance.

That is, the parity check matrix initial value table indicates at leastthe positions of the elements “1” of the information matrix H_(A) forevery 360 columns (unit size P).

In addition, examples of the parity check matrix H include a paritycheck matrix which is defined by, for example, DVB-T.2 and in which the(entire) parity matrix H_(T) has the dual diagonal structure and aparity check matrix which is suggested by CRC/ETRI and in which a partof the parity matrix H_(T) has the dual diagonal structure and theremaining portion is a diagonal matrix (unit matrix).

Hereinafter, a method for expressing the parity check matrix initialvalue table indicating the parity check matrix which is defined by, forexample, DVB-T.2 and in which the parity matrix H_(T) has the dualdiagonal structure is referred to as a DVB method and a method forexpressing the parity check matrix initial value table indicating theparity check matrix which is suggested by CRC/ETRI is referred to as anETRI method.

FIG. 20 is a diagram illustrating an example of the parity check matrixinitial value table based on the DVB method.

That is, FIG. 20 illustrates a parity check matrix initial value tablecorresponding to the parity check matrix H which is defined by theDVB-T.2 standard and has a code length N of 16200 bits and a coding rate(a coding rate in DVB-T.2) r of 1/4.

The parity check matrix generation unit 613 (FIG. 18) calculates theparity check matrix H, using the parity check matrix initial value tablebased on the DVB method, as follows.

FIG. 21 is a diagram illustrating a method for calculating the paritycheck matrix H from the parity check matrix initial value table based onthe DVB method.

That is, FIG. 21 illustrates a parity check matrix initial value tablecorresponding to a parity check matrix H which is defined by the DVB-T.2standard and has a code length N of 16200 bits and a coding rate r of2/3.

The parity check matrix initial value table based on the DVB method is atable which represents the positions of elements “1” of the entireinformation matrix H_(A) corresponding to the information length K whichcorresponds to the code length N and the coding rate r of the LDPC codefor every 360 columns (unit size P). In an i-th row of the table, therow numbers of the elements “1” in a (1+360×(i−1))-th column of theparity check matrix H (the row numbers of the elements “1” in the firstrow of the parity check matrix H are 0) are arranged. The row numberscorrespond to the number of column weights of the (1+360×(i−1))-thcolumn.

The parity matrix H_(T) (FIG. 10) corresponding to the parity length Min the parity check matrix H based on the DVB method is decided to havethe dual diagonal structure illustrated in FIG. 15. Therefore, when theinformation matrix H_(A) (FIG. 10) corresponding to the informationlength K can be calculated using the parity check matrix initial valuetable, it is possible to calculate the parity check matrix H.

The number of rows k+1 in the parity check matrix initial value tablebased on the DVB method varies depending on the information length K.

Formula (9) is established between the information length K and thenumber of rows k+1 in the parity check matrix initial value table.

K=(k+1)×360   (9)

Here, “360” in Formula (9) is the unit size P described in FIG. 16.

In the parity check matrix initial value table illustrated in FIG. 21,13 numerical values are arranged from the first row to the third row and3 numerical values are arranged from the fourth row to a (k+1)-th row (a30th row in FIG. 21).

Therefore, in the parity check matrix H calculated from the parity checkmatrix initial value table illustrated in FIG. 21, the weight of each ofthe first column to a (1+360×(3−1)−1)-th column is 13 and the weight ofeach of a (1+360×(3−1))-th column to a K-th column is 3.

In the first row of the parity check matrix initial value tableillustrated in FIG. 21, 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297,2481, 3369, 3451, 4620, and 2622 are written, which indicates thatelements in the rows having row numbers 0, 2084, 1613, 1548, 1286, 1460,3196, 4297, 2481, 3369, 3451, 4620, and 2622 are 1 (and the otherelements are 0) in the first column of the parity check matrix H.

In the second row of the parity check matrix initial value tableillustrated in FIG. 21, 1, 122, 1516, 3448, 2880, 1407, 1847, 3799,3529, 373, 971, 4358, and 3108 are written, which indicates thatelements in the rows having row numbers 1, 122, 1516, 3448, 2880, 1407,1847, 3799, 3529, 373, 971, 4358, and 3108 are 1 in a 361st(=(1+360×(2−1)-th) column of the parity check matrix H.

As such, the parity check matrix initial value table indicates thepositions of elements “1” in the information matrix H_(A) of the paritycheck matrix H for every 360 columns.

The columns other than the (1+360×(i−1))-th column in the parity checkmatrix H, that is, a (2+360×(i−1))-th column to a (360×i)-th column arearranged by cyclically shifting elements “1” of the (1+360×(i−1))-thcolumn determined by the parity check matrix initial value table in thedownward direction (the downward direction of the columns) according tothe parity length M.

That is, for example, a (2+360×(i−1))-th column is obtained bycyclically shifting (1+360×(i −1))-th column in the downward directionby M/360 (=q) and the next (3+360×(i−1))-th column is obtained bycyclically shifting the (1+360×(i−1))-th column in the downwarddirection by 2×M/360(=2×q) (by cyclically shifting (2+360×(i−1))-thcolumn in the downward direction by M/360(=q)).

When a numerical value in an i-th row (an i-th row from the upper side)and a j-th column (a j-th column from the left side) of the parity checkmatrix initial value table is represented by h_(i,j) and the row numberof a j-th element “1” in a w-th column of the parity check matrix H isrepresented by H_(w-j), the row numbers H_(w-j) of elements “1” in thew-th column, which is other than the (1+360×(i−1))-th column in theparity check matrix H can be calculated by Formula (10).

H _(w-j)=mod{h _(i,j)+mod((w−1), P)×q, M)   (10)

Here, mod(x, y) is the remainder when x is divided by y.

In addition, P is the above-mentioned unit size. In this embodiment, forexample, similarly to the DVB-S.2 standard, the DVB-T.2 standard, andthe DVB-C.2 standard, P is 360. In addition, q is a value of M/360 thatis obtained by dividing the parity length M by the unit size P (=360).

The parity check matrix generation unit 613 (FIG. 18) specifies the rownumbers of elements “1” in the (360×(i−1))-th column of the parity checkmatrix H using the parity check matrix initial value table.

In addition, the parity check matrix generation unit 613 (FIG. 18)calculates the row numbers H_(w-j) of the elements “1” in the w-thcolumn other than the (1+360×(i−1))-th column of the parity check matrixH, according to Formula (10), and generates a parity check matrix H inwhich the elements with the obtained row numbers are 1.

FIG. 22 is a diagram illustrating the structure of a parity check matrixbased on the ETRI method.

The parity check matrix based on the ETRI method includes an A matrix, aB matrix, a C matrix, a D matrix, and a Z matrix.

The A matrix is a matrix of g rows and K columns which is located on theupper left side of the parity check matrix and is represented by apredetermined value g and the information length K of the LDPC code=thecode length N×the coding rate r.

The B matrix is a matrix of g rows and g columns which is adjacent onthe right side of the A matrix and has a dual diagonal structure.

The C matrix is a matrix of N−K−g rows and K+g columns which is adjacentto the lower side of the A matrix and the B matrix.

The D matrix is a matrix of N−K−g rows and N−K−g columns which is a unitmatrix and is adjacent to the right side of the C matrix.

The Z matrix is a zero matrix (0 matrix) of g rows and N−K−g columns andis adjacent to the right side of the B matrix.

In the parity check matrix based on the ETRI method including the A to Dmatrices and the Z matrix, the A matrix and a portion of the C matrixform an information matrix, and the B matrix, the remaining portion ofthe C matrix, the D matrix, and the Z matrix form a parity matrix.

Since the B matrix is a matrix having the dual diagonal structure andthe D matrix is the unit matrix, a portion (B matrix) of the paritymatrix of the parity check matrix based on the ETRI method has the dualdiagonal structure and the remaining portion (D matrix) is a diagonalmatrix (unit matrix).

Similarly to the information matrix of the parity check matrix based onthe DVB method, the A matrix and the C matrix have a cyclic structurefor every 360 columns (unit size P) and the parity check matrix initialvalue table based on the ETRI method indicates the positions of elements“1” of the A matrix and the C matrix for every 360 columns.

As described above, since the A matrix and a portion of the C matrixform the information matrix, the parity check matrix initial value tablebased the ETRI method which indicates the positions of elements “1” inthe A matrix and the C matrix for every 360 columns can indicate atleast the positions of elements “1” in the information matrix H_(A) forevery 360 columns.

FIG. 23 is a diagram illustrating an example of the parity check matrixinitial value table based on the ETRI method.

That is, FIG. 23 illustrates an example of a parity check matrix initialvalue table corresponding to a parity check matrix having a code lengthN of 50 bits and a coding rate r of 1/2.

The parity check matrix initial value table based on the ETRI method isa table which indicates the positions of the elements “1” in the A and Cmatrices for each unit size P. In the i-th row of the table, the rownumbers of elements “1” in a (1+P×(i−1))-th column of the parity checkmatrix (the row numbers of elements “1” in the first row of the paritycheck matrix H are 0) are arranged. The row numbers correspond to thenumber of column weights of the (1+P×(i−1))-th column.

Here, for simplicity of explanation, it is assumed that the unit size Pis, for example, 5.

For the parity check matrix based on the ETRI method, there areparameters g=M₁, M₂, Q₁, and Q₂.

Here, g=M₁ is a parameter for determining the size of the B matrix andis a multiple of the unit size P. When g=M₁ is adjusted, the performanceof the LDPC code is changed. When the parity check matrix is determined,g=M₁ is adjusted to a predetermined value. Here, 15 which is three timesthe unit size P (=5) is used as g=M₁.

M₂ has a value M−M₁ obtained by subtracting M₁ from the parity length M.

Here, the information length K is N×r=50×1/2=25 and the parity length Mis N−K=50−25=25. Therefore, M₂ is M−M_(i)=25−15=10.

Q₁ is calculated according to a formula Q₁=M₁/P and indicates the numberof cyclic shifts (the number of rows) in the A matrix.

In other words, columns other than a (1+P×(i−1))-th column, that is, the(2+P×(i−1))-th to (P×i)-th columns in the A matrix of the parity checkmatrix based on the ETRI method are arranged by cyclically shiftingelements “1” in the (1+360×(i−1))-th column determined by the paritycheck matrix initial value table in the downward direction (the downwarddirection of the column), and Q₁ indicates the number of cyclic shiftsin the A matrix.

Q2 is calculated according to a formula Q₂=M₂/P and indicates the numberof cyclic shifts (the number of rows) in the C matrix.

That is, in other words, columns other than a (1+P×(i−1))-th column,that is, the (2+P×(i−1))-th to (P×i)-th columns in the C matrix of theparity check matrix based on the ETRI method are arranged by cyclicallyshifting elements “1” in the (1+360×(i−1))-th column determined by theparity check matrix initial value table in the downward direction (thedownward direction of the column), and Q₂ indicates the number of cyclicshifts in the C matrix.

Here, Q₁ is M₁/P=15/5=3 and Q₂ is M₂/P=10/5=2.

In the parity check matrix initial value table illustrated in FIG. 23,three numerical values are arranged in the first and second rows and onenumerical value is arranged in the third to fifth rows. According to thearrangement of the numerical values, for the column weight of the paritycheck matrix calculated from the parity check matrix initial value tableillustrated in FIG. 23, the weight of the first to (1+5×(2−1)−1)-thcolumns is 3 and the weight of the (1+5×(2−1))-th to fifth columns is 1.

That is, 2, 6, and 18 are arranged in the first row of the parity checkmatrix initial value table illustrated in FIG. 23, which shows thatelements in rows with row numbers 2, 6, and 18 are 1 (and the otherelements are 0) in the first column of the parity check matrix.

Here, in this case, the A matrix is a matrix of 15 rows and 25 columns(g rows and K columns) and the C matrix is a matrix of 10 rows and 40columns (N−K−g rows and K+g columns). Therefore, rows with row numbers 0to 14 in the parity check matrix are rows of the A matrix, and rows withrow numbers 15 to 24 in the parity check matrix are rows of the Cmatrix.

Therefore, among rows with row numbers 2, 6, and 18 (hereinafter,referred to as rows #2, #6, and #18), the rows #2 and #6 are rows of theA matrix, and the row #18 is a row of the C matrix.

In addition, 2, 10, and 19 are arranged in the second row of the paritycheck matrix initial value table illustrated in FIG. 23, which showsthat elements in rows #2, #10, and #19 are 1 in the 6th (=1+5×(2−1))column of the parity check matrix.

Here, in the 6th (=1+5×(2−1)) column of the parity check matrix, amongthe rows #2, #10, and #19, the rows #2 and #10 are rows of the A matrixand the row #19 is a row of the C matrix.

22 is arranged in the third row of the parity check matrix initial valuetable illustrated in FIG. 23, which shows that elements in the row #22are 1 in the 11th (=1+5×(3−1)) column of the parity check matrix.

Here, in the 11th (=1+5×(3−1)) column of the parity check matrix, therow #22 is a row of the C matrix.

Similarly, 19 in the fourth row of the parity check matrix initial valuetable illustrated in FIG. 23 indicates that elements in the row #19 are1 in the 16th (=1+5×(4−1)) column of the parity check matrix, and 15 inthe fifth row of the parity check matrix initial value table illustratedin FIG. 23 indicates that elements in the row #15 are 1 in the 21st(=1+5×(5−1)) column of the parity check matrix.

As described above, the parity check matrix initial value tablerepresents the positions of the elements “1” in the A and C matrices ofthe parity check matrix for every unit size P (=5 columns).

Columns other than the (1+5×(i−1))-th columns, that is, the(2+5×(i−1))-th to (5×i)-th columns in the A and C matrices are arrangedby cyclically shifting elements “1” in the (1+5×(i−1))-th columndetermined by the parity check matrix initial table in the downwarddirection (the downward direction of the columns) according to theparameters Q₁and Q₂.

That is, for example, the (2+5×(i−1))-th column of the A matrix isobtained by cyclically shifting the (1+5×(i−1))-th column in thedownward direction by Q₁(=3) and the next (3+5×(i−1))-th column isobtained by cyclically shifting the (1+5×(i−1))-th column in thedownward direction by 2×Q₁(=2×3) (by cyclically shifting the(2+5×(i−1))-th column in the downward direction by Q₁).

For example, the (2+5×(i−1))-th column of the C matrix is obtained bycyclically shifting the (1+5×(i−1))-th column in the downward directionby Q₂ (=2) and the next (3+5×(i−1))-th column is obtained by cyclicallyshifting the (1+5×(i−1))-th column in the downward direction by2×Q₂(=2×2) (by cyclically shifting the (2+5×(i−1))-th column in thedownward direction by Q₂).

FIG. 24 is a diagram illustrating the A matrix that is generated fromthe parity check matrix initial value table illustrated in FIG. 23.

In the A matrix illustrated in FIG. 24, elements in rows #2 and #6 andthe 1st (=1+5×(1−1)) column are 1 on the basis of the first row of theparity check matrix initial value table illustrated in FIG. 23.

The 2nd (=2+5×(1−1)) to 5th (=5+5×(1−1)) columns are obtained bycyclically shifting the previous columns in the downward direction byQ₁=3.

In the A matrix illustrated in FIG. 24, elements in rows #2 and #10 andthe 6th (=1+5×(2−1)) column are 1 on the basis of the second row of theparity check matrix initial value table illustrated in FIG. 23.

The 7th (=2+5×(2−1)) to 10th (=5+5×(2−1)) columns are obtained bycyclically shifting the previous columns in the downward direction byQ₁=3.

FIG. 25 is a diagram illustrating parity interleaving for the B matrix.

The parity check matrix generation unit 613 (FIG. 18) generates the Amatrix, using the parity check matrix initial value table, and arrangesthe B matrix with the dual diagonal structure so as to be adjacent tothe right side of the A matrix. Then, the parity check matrix generationunit 613 regards the B matrix as a parity matrix and performs parityinterleaving such that adjacent elements “1” of the B matrix having thedual diagonal structure are separated from each other by the unit size P(=5) in the row direction.

FIG. 25 illustrates the A matrix and the B matrix after the parityinterleaving for the B matrix.

FIG. 26 is a diagram illustrating the C matrix which is generated fromthe parity check matrix initial value table illustrated in FIG. 23.

In the C matrix illustrated in FIG. 26, an element in a row #18 and the1st (=1+5×(1−1)) column of the parity check matrix are 1 on the basis ofthe first row of the parity check matrix initial value table illustratedin FIG. 23.

The 2nd (=2+5×(1−1)) to 5th (=5+5×(1−1)) columns of the C matrix areobtained by cyclically shifting the previous columns by Q₂ (=2).

In the C matrix illustrated in FIG. 26, an element in a row #19 and the6th (=1+5×(2−1)) column, an element in a row #22 and the 11th(=1+5×(3−1)) column, an element in a row #19 and the 16th (=1+5×(4−1))column, and an element in a row #15 and the 21st (=1+5×(5−1)) column inthe parity check matrix are 1 on the basis of the second to fifth rowsof the parity check matrix initial value table illustrated in FIG. 23.

The 7th (=2+5×(2−1)) to 10th (=5+5×(2−1)) columns, the 12th (=2+5×(3−1))to 15th (=5+5×(3−1)) columns, the 17th (=2+5×(4−1)) to 20th (=5+5×(4−1))columns, and the 22nd (=2+5×(5−1)) to 25th (=5+5×(5−1)) columns areobtained by cyclically shifting the previous columns in the downwarddirection by Q₂ (=2).

The parity check matrix generation unit 613 (FIG. 18) generates the Cmatrix, using the parity check matrix initial value table, and arrangesthe C matrix below the A matrix and the (parity-interleaved) B matrix.

In addition, the parity check matrix generation unit 613 arranges the Zmatrix so as to be adjacent to the right side of the B matrix, arrangesthe D matrix so as to be adjacent to the right side of the C matrix, andgenerates the parity check matrix illustrated in FIG. 26.

FIG. 27 is a diagram illustrating parity interleaving for the D matrix.

After generating the parity check matrix illustrated in FIG. 26, theparity check matrix generation unit 613 regards the D matrix as a paritymatrix and performs parity interleaving (only for the D matrix) suchthat elements “1” in the odd-numbered rows and the next even-numberedrows of the D matrix, which is the unit matrix, are separated from eachother in the row direction by the unit size P (=5).

FIG. 27 illustrates a parity check matrix after parity interleaving isfor the D matrix in the parity check matrix illustrated in FIG. 26.

For example, (the coding parity calculation unit 615 (FIG. 18) of) theLDPC encoder 115 performs LDPC coding (the generation of an LDPC code),using the parity check matrix illustrated in FIG. 27.

Here, the LDPC code which is generated using the parity check matrixillustrated in FIG. 27 is an LDPC code subjected to the parityinterleaving. Therefore, the parity interleaver 23 (FIG. 9) does notneed to perform parity interleaving for the LDPC code which has beengenerated using the parity check matrix illustrated in FIG. 27.

FIG. 28 is a diagram illustrating a parity check matrix that is obtainedby performing, as parity deinterleaving, a column permutation processwhich returns the parity-interleaved matrices to the original state forthe B matrix, a portion of the C matrix (a portion of the C matrix whichis arranged below the B matrix), and the D matrix in the parity checkmatrix illustrated in FIG. 27.

The LDPC encoder 115 can perform LDPC coding (the generation of the LDPCcode), using the parity check matrix illustrated in FIG. 28.

When LDPC coding is performed using the parity check matrix illustratedin FIG. 28, an LDPC code that has not been subjected to parityinterleaving is obtained according to the LDPC coding. Therefore, whenLDPC coding is performed using the parity check matrix illustrated inFIG. 28, the parity interleaver 23 (FIG. 9) performs parityinterleaving.

FIG. 29 is a diagram illustrating a transformed parity check matrixobtained by performing row permutation for the parity check matrixillustrated in FIG. 27.

The transformed parity check matrix is represented by a combination of aP×P unit matrix, a quasi unit matrix obtained by substituting one ormore is of the unit matrix with 0, a shifted matrix obtained bycyclically shifting the unit matrix or the quasi unit matrix, a summatrix which is the sum of two or more of the unit matrix, the quasiunit matrix, and the shifted matrix, and a P×P zero matrix, which willbe described below.

The use of the transformed parity check matrix to decode the LDPC codemakes it possible to adopt an architecture in which the check nodeoperation and the variable node operation are simultaneously performed Ptimes during the decoding of the LDPC code, which will be describedbelow.

<New LDPC Code>

In recent years, a terrestrial digital television broadcasting standard,which is called ATSC3.0, has been developed.

A new LDPC code (hereinafter, also referred to as a new LDPC code) whichcan be used in ATSC3.0 and other data transmission standards will bedescribed.

Examples of the new LDPC code include an LDPC code based on the DVBmethod or an LDPC code based on the ETRI method which corresponds to aparity check matrix having a cyclic structure and has a unit size P of360 that is equal to the unit size in, for example, the DVB-T.2standard.

The LDPC encoder 115 (FIG. 8 and FIG. 18) can perform LDPC coding forthe new LDPC code, using a parity check matrix that is calculated from aparity check matrix initial value table of the new LDPC code having acode length N of 16 kbits or 64 kbits and a coding rate r of 5/15, 6,15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, or 13/15, which will bedescribed below.

In this case, the storage unit 602 of the LDPC encoder 115 (FIG. 8)stores the parity check matrix initial value table of the new LDPC code.

FIG. 30 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 8/15 (hereinafter, also referred to as a Sony code with(16 k, 8/15)) which is suggested by the inventors.

FIG. 31 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 10/15 (hereinafter, also referred to as a Sony codewith (16 k, 10/15)) which is suggested by the inventors.

FIG. 32 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 12/15 (hereinafter, also referred to as a Sony codewith (16 k, 12/15)) which is suggested by the inventors.

FIGS. 33, 34, and 35 are diagrams illustrating an example of a paritycheck matrix initial value table based on the DVB method with respect toa parity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 7/15 (hereinafter, also referred to as aSony code with (64 k, 7/15)) which is suggested by the inventors.

FIG. 34 is a diagram subsequent to FIG. 33 and FIG. 35 is a diagramsubsequent to FIG. 34.

FIGS. 36, 37, and 38 are diagrams illustrating an example of a paritycheck matrix initial value table based on the DVB method with respect toa parity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 9/15 (hereinafter, also referred to as aSony code with (64 k, 9/15)) which is suggested by the inventors.

FIG. 37 is a diagram subsequent to FIG. 36 and FIG. 38 is a diagramsubsequent to FIG. 37.

FIGS. 39, 40, 41, and 42 are diagrams illustrating an example of aparity check matrix initial value table based on the DVB method withrespect to a parity check matrix of a new LDPC code having a code lengthN of 64 kbits and a coding rate r of 11/15 (hereinafter, also referredto as a Sony code with (64 k, 11/15)) which is suggested by theinventors.

FIG. 40 is a diagram subsequent to FIG. 39, FIG. 41 is a diagramsubsequent to FIG. 40, and FIG. 42 is a diagram subsequent to FIG. 41.

FIGS. 43, 44, 45, and 46 are diagrams illustrating an example of aparity check matrix initial value table based on the DVB method withrespect to a parity check matrix of a new LDPC code having a code lengthN of 64 kbits and a coding rate r of 13/15 (hereinafter, also referredto as a Sony code with (64 k, 13/15)) which is suggested by theinventors.

FIG. 44 is a diagram subsequent to FIG. 43, FIG. 45 is a diagramsubsequent to FIG. 44, and FIG. 46 is a diagram subsequent to FIG. 45.

FIGS. 47 and 48 are diagrams illustrating an example of a parity checkmatrix initial value table based on the DVB method with respect to aparity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 6/15 (hereinafter, also referred to as aSamsung code with (64 k, 6/15)) which is suggested by SamsungElectronics Co., Ltd.

FIG. 48 is a diagram subsequent to FIG. 47.

FIGS. 49, 50, and 51 are diagrams illustrating an example of a paritycheck matrix initial value table based on the DVB method with respect toa parity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 8/15 (hereinafter, also referred to as aSamsung code with (64 k, 8/15)) which is suggested by SamsungElectronics Co., Ltd.

FIG. 50 is a diagram subsequent to FIG. 49 and FIG. 51 is a diagramsubsequent to FIG. 50.

FIGS. 52, 53, and 54 are diagrams illustrating an example of a paritycheck matrix initial value table based on the DVB method with respect toa parity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 12/15 (hereinafter, also referred to as aSamsung code with (64 k, 12/15)) which is suggested by SamsungElectronics Co., Ltd.

FIG. 53 is a diagram subsequent to FIG. 52 and FIG. 54 is a diagramsubsequent to FIG. 53.

FIG. 55 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 6/15 (hereinafter, also referred to as an LGE code with(16 k, 6/15)) which is suggested by LG Electronics Inc.

FIG. 56 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 7/15 (hereinafter, also referred to as an LGE code with(16 k, 7/15)) which is suggested by LG Electronics Inc.

FIG. 57 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 9/15 (hereinafter, also referred to as an LGE code with(16 k, 9/15)) which is suggested by LG Electronics Inc.

FIG. 58 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 11/15 (hereinafter, also referred to as an LGE codewith (16 k, 11/15)) which is suggested by LG Electronics Inc.

FIG. 59 is a diagram illustrating an example of a parity check matrixinitial value table based on the DVB method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 13/15 (hereinafter, also referred to as an LGE codewith (16 k, 13/15)) which is suggested by LG Electronics Inc.

FIGS. 60, 61, and 62 are diagrams illustrating an example of a paritycheck matrix initial value table based on the DVB method with respect toa parity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 10/15 (hereinafter, also referred to as anLGE code with (64 k, 10/15)) which is suggested by LG Electronics Inc.

FIG. 61 is a diagram subsequent to FIG. 60 and FIG. 62 is a diagramsubsequent to FIG. 61.

FIGS. 63, 64, and 65 are diagrams illustrating an example of a paritycheck matrix initial value table based on the DVB method with respect toa parity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 9/15 (hereinafter, also referred to as aNERC code with (64 k, 9/15)) which is suggested by North AmericanElectric Reliability Corporation (NERC).

FIG. 64 is a diagram subsequent to FIG. 63 and FIG. 65 is a diagramsubsequent to FIG. 64.

FIG. 66 is a diagram illustrating an example of a parity check matrixinitial value table based on the ETRI method with respect to a paritycheck matrix of a new LDPC code having a code length N of 16 kbits and acoding rate r of 5/15 (hereinafter, also referred to as an ETRI codewith (16 k, 5/15)) which is suggested by CRC/ETRI.

FIGS. 67 and 68 are diagrams illustrating an example of a parity checkmatrix initial value table based on the ETRI method with respect to aparity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 5/15 (hereinafter, also referred to as anETRI code with (64 k, 5/15)) which is suggested by CRC/ETRI.

FIG. 68 is a diagram subsequent to FIG. 67.

FIGS. 69 and 70 are diagrams illustrating an example of a parity checkmatrix initial value table based on the ETRI method with respect to aparity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 6/15 (hereinafter, also referred to as anETRI code with (64 k, 6/15)) which is suggested by CRC/ETRI.

FIG. 70 is a diagram subsequent to FIG. 69.

FIGS. 71 and 72 are diagrams illustrating an example of a parity checkmatrix initial value table based on the ETRI method with respect to aparity check matrix of a new LDPC code having a code length N of 64kbits and a coding rate r of 7/15 (hereinafter, also referred to as anETRI code with (64 k, 7/15)) which is suggested by CRC/ETRI.

FIG. 72 is a diagram subsequent to FIG. 71.

Among the LDPC codes, particularly, the Sony codes are high-performanceLDPC codes.

Here, the high-performance LDPC code means an LDPC code which isobtained from an appropriate parity check matrix H.

The appropriate parity check matrix H is, for example, a parity checkmatrix that satisfies a predetermined condition for reducing a bit errorrate (BER) (and a frame error rate (FER)) when an LDPC code obtainedfrom the parity check matrix H is transmitted at low E_(s)/N₀ orE_(b)/N_(o) (a signal-to-noise power ratio per bit).

For example, the appropriate parity check matrix H can be calculated bya simulation that measures the BER when the LDPC codes obtained fromvarious parity check matrices satisfying a predetermined condition aretransmitted at low E_(s)/N_(o).

Examples of the predetermined condition to be satisfied by theappropriate parity check matrix H include a condition in which ananalysis result obtained by a code performance analysis method that iscalled density evolution is excellent and a condition in which a loop ofelements “1” is not present and which is called cycle 4.

Here, in the information matrix H_(A), it has been known that the LDPCcode decoding performance deteriorates when elements “1” are dense as incycle 4. Therefore, a condition in which cycle 4 is not present isrequired as the predetermined condition to be satisfied by theappropriate parity check matrix H.

Here, the predetermined condition to be satisfied by the appropriateparity check matrix H can be arbitrarily determined from the viewpointof, for example, improving the LDPC code decoding performance andfacilitating (simplifying) the LDPC code decoding process.

FIGS. 73 and 74 are diagrams illustrating density evolution that canobtain the analysis result as the predetermined condition to besatisfied by the appropriate parity check matrix H.

The density evolution is a code analysis method that calculates theexpected value of the error probability of the entire LDPC code(ensemble) with a code length N of ∞ which is characterized by a degreesequence, which will be described below.

For example, when a noise variance is gradually increased from 0 on theAWGN channel, the expected value of the error probability of a certainensemble is 0 at the beginning. However, when the noise variance isequal to or greater than a certain threshold value, the expected valueis not 0.

According to the density evolution, the comparison of the thresholdvalue of the noise variance (hereinafter, also referred to as aperformance threshold value) at which the expected value of the errorprobability is not 0 makes it possible to determine whether theperformance of the ensemble is high or low (the appropriateness of theparity check matrix).

For a specific LDPC code, when an ensemble to which the LDPC codebelongs is determined and density evolution is performed for theensemble, it is possible to roughly expect the performance of the LDPCcode.

Therefore, when a high-performance ensemble is found, a high-performanceLDPC can be found from the LDPC codes belonging to the ensemble.

Here, the above-mentioned degree sequence indicates the proportion ofthe variable nodes or the check nodes having the weight of each value tothe code length N of the LDPC code.

For example, a regular (3, 6) LDPC code with a coding rate of 1/2belongs to an ensemble characterized by a degree sequence in which theweight (column weight) of all of the variable nodes is 3 and the weight(row weight) of all of the check nodes is 6.

FIG. 73 illustrates a Tanner graph of the ensemble.

In the Tanner graph illustrated in FIG. 73, there are N variable nodeswhich are represented by a circle (symbol ◯) in FIG. 73 and of which thenumber is equal to the code length N and there are N/2 check nodes whichare represented by a rectangle (symbol □) and of which the number isequal to a value obtained by multiplying the code length N by a codingrate of 1/2.

Three edges, of which the number is equal to the column weight, areconnected to each variable node. Therefore, a total of 3N edges areconnected to N variable nodes.

In addition, six edges, of which the number is equal to the row weight,are connected to each check node. Therefore, a total of 3N edges areconnected to N/2 check nodes.

In addition, there is one interleaver in the Tanner graph illustrated inFIG. 73.

The interleaver randomly rearranges 3N edges connected with N variablenodes and connects each of the rearranged edges to any one of 3N edgesconnected to N/2 check nodes.

There are (3N)! (=(3N)×(3N−1)× . . . ×1) rearrangement patterns torearrange 3N edges connected to

N variable nodes in the interleaver. Therefore, an ensemblecharacterized by the degree sequence in which the weight of all of thevariable nodes is 3 and the weight of all of the check nodes is 6 is aset of (3N)! LDPC codes.

In a simulation for finding a high-performance LDPC code (appropriateparity check matrix), a multi-edge-type ensemble was used in densityevolution.

In the multi-edge type, an interleaver though which the edges connectedto the variable nodes and the edges connected to the check nodes pass isdivided into a plurality of portions (multiple edges). Therefore, theensemble is characterized more strictly.

FIG. 74 illustrates an example of a Tanner graph of the multi-edge-typeensemble.

There are two interleavers, that is, a first interleaver and a secondinterleaver, in the Tanner graph illustrated in the FIG. 74.

In the Tanner graph chart illustrated in the FIG. 74, there are v1variable nodes each of which has one edge connected to the firstinterleaver and no edge connected to the second interleaver, v2 variablenodes each of which has one edge connected to the first interleaver andtwo edges connected to the second interleaver, and v3 variable nodeseach of which has no edge connected to the first interleaver and twoedges connected to the second interleaver.

In addition, in the Tanner graph chart illustrated in the FIG. 74, thereare c1 check nodes each of which has two edges connected to the firstinterleaver and no edge connected to the second interleaver, c2 checknodes each of which has two edges connected to the first interleaver andtwo edges connected to the second interleaver, and c3 check nodes eachof which has no edge connected to the first interleaver and three edgesconnected to the second interleaver.

For example, the density evolution and the mounting thereof aredescribed in “On the Design of Low-Density Parity-Check Codes within0.0045 dB of the Shannon Limit”, S. Y. Chung, G. D. Forney, T. J.Richardson, R. Urbanke, IEEE Communications Leggers, VOL. 5, NO. 2,February 2001.

In a simulation for calculating (a parity check matrix initial valuetable of) a Sony code, by the multi-edge-type density evaluation isperformed to find an ensemble in which a performance threshold value,which is E_(b)/N₀ (a signal-to-noise power ratio per bit) where BER isreduced (decreased), is equal to or less than a predetermined value andan LDPC code that reduce the BER when one or more quadrature modulationmethods, such as QPSK, are used is selected as a high-performance LDPCcode from LDPC codes belonging to the ensemble.

The parity check matrix initial value table of the Sony code iscalculated by the above-mentioned simulation.

Therefore, the Sony code obtained from the parity check matrix initialvalue table makes it possible to ensure high communication quality indata transmission.

FIG. 75 is a diagram illustrating a parity check matrix H calculatedfrom the parity check matrix initial value table of Sony codes with (16k, 8/15), (16 k, 10/15), and (16 k, 12/15) (hereinafter, also referredto as a “parity check matrix H of Sony codes with (16 k, 8/15), (16 k,10/15), and (16 k, 12/15)”).

Each of the minimum cycle lengths of the parity check matrix H of theSony codes with (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15) isgreater than cycle 4 and cycle 4 is not present (a loop of elements “1”with a loop length of 4). Here, the minimum cycle length (girth) meansthe minimum value of the length of a loop (loop length) formed byelements “1” in the parity check matrix H.

In addition, the performance threshold value of the Sony code with (16k, 8/15) is 0.805765. The performance threshold value of the Sony codewith (16 k, 10/15) is 2.471011. The performance threshold value of theSony code with (16 k, 12/15) is 4.269922.

In the parity check matrix H of the Sony codes with (16 k, 8/15), (16 k,10/15), and (16 k, 12/15), the weight of KX1 columns from the firstcolumn is X1, the weight of the next KX2 columns is X2, the weight ofthe next KY1 columns is Y1, the weight of the next KY2 columns is Y2,the weight of the next M−1 columns is 2, and the weight of the finalcolumn is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=16200 bits)of the Sony codes with (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

The number of columns KX1, KX2, KY1, KY2, and M and the column weightsX1, X2, Y1, and Y2 in the parity check matrix H of the Sony codes with(16 k, 8/15), (16 k, 10/15), and (16 k, 12/15) are set as illustrated inFIG. 75.

For the parity check matrix H of the Sony codes with (16 k, 8/15), (16k, 10/15), and (16 k, 12/15), similarly to the parity check matricesdescribed in FIGS. 12 and 13, a column that is closer to on the headside (left side) tends to have a greater column weight. Therefore, acode bit that is closer to the head of the Sony code tends to havehigher tolerance to errors (to have a higher error tolerance).

According to the simulation performed by the inventors, a high BER/FERis obtained for the Sony codes with (16k, 8/15), (16k, 10/15), and (16k,12/15). Therefore, it is possible to ensure high communication qualityin data transmission using the Sony codes with (16k, 8/15), (16k,10/15), and (16k, 12/15).

FIG. 76 is a diagram illustrating of a parity check matrix H of Sonycodes with (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

Each of the minimum cycle lengths of the parity check matrix H of theSony codes with (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k,13/15) is greater than cycle 4. Therefore, cycle 4 is not present.

In addition, the performance threshold value of the Sony code with (64k, 7/15) is −0.093751. The performance threshold value of the Sony codewith (64 k, 9/15) is 1.658523. The performance threshold value of theSony code with (64 k, 11/15) is 3.351930. The performance thresholdvalue of the Sony code with (64 k, 13/15) is 5.301749.

In the parity check matrix H of the Sony codes with (64k, 7/15), (64k,9/15), (64k, 11/15), and (64k, 13/15), the weight of KX1 columns fromthe first column is X1, the weight of the next KX2 columns is X2, theweight of the next KY1 columns is Y1, the weight of the next KY2 columnsis Y2, the weight of the next M−1 columns is 2, and the weight of thefinal column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=64800 bits)of the Sony codes with (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k,13/15).

The number of columns KX1, KX2, KY1, KY2, and M and the column weightsX1, X2, Y1, and Y2 in the parity check matrix H of the Sony codes with(64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15) are set asillustrated in FIG. 76.

For the parity check matrix H of the Sony codes with (64k, 7/15), (64k,9/15), (64k, 11/15), and (64k, 13/15), similarly to the parity checkmatrices described in FIGS. 12 and 13, a column that is closer to thehead side (left side) tends to have a greater column weight. Therefore,a code bit that is closer to the head of the Sony code tends to have ahigher error tolerance.

According to the simulation performed by the inventors, a high BER/FERwas obtained for the Sony codes with (64k, 7/15), (64k, 9/15), (64k,11/15), and (64k, 13/15). Therefore, it is possible to ensure highcommunication quality in data transmission using the Sony codes with(64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15).

FIG. 77 is a diagram illustrating a parity check matrix H of Samsungcodes with (64k, 6/15), (64k, 8/15), and (64k, 12/15).

In the parity check matrix H of the Samsung code with (64k, 6/15), (64k,8/15), and (64k, 12/15), the weight of KX1 columns from the first columnis X1, the weight of the next KX2 columns is X2, the weight of the nextKY1 columns is Y1, the weight of the next KY2 columns is Y2, the weightof the next M−1 columns is 2, and the weight of the final column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=64800 bits)of the Samsung codes with (64k, 6/15), (64k, 8/15), and (64k, 12/15).

The number of columns KX1, KX2, KY1, KY2, and M and the column weightsX1, X2, Y1, and Y2 in the parity check matrix H of the Samsung codeswith (64k, 6/15), (64k, 8/15), and (64k, 12/15) are set as illustratedin FIG. 77.

FIG. 78 is a diagram illustrating a parity check matrix H of LGE codeswith (16k, 6/15), (16k, 7/15), (16k, 9/15), (16k, 11/15), and (16k,13/15).

In the parity check matrix H of the LGE codes with (16k, 6/15), (16k,7/15), (16k, 9/15), (16k, 11/15), and (16k, 13/15), the weight of KX1columns from the first column is X1, the weight of the next KX2 columnsis X2, the weight of the next KY1 columns is Y1, the weight of the nextKY2 columns is Y2, the weight of the next M−1 columns is 2, and theweight of the final column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=16200 bits)of the LGE codes with (16k, 6/15), (16k, 7/15), (16k, 9/15), (16k,11/15), and (16k, 13/15).

The number of columns KX1, KX2, KY1, KY2, and M and the column weightsX1, X2, Y1, and Y2 in the parity check matrix H of the LGE codes with(16k, 6/15), (16k, 7/15), (16k, 9/15), (16k, 11/15), and (16k, 13/15)are set as illustrated in FIG. 78.

FIG. 79 is a diagram illustrating a parity check matrix H of an LGE codewith (64k, 10/15).

In the parity check matrix H of the LGE code with (64k, 10/15), theweight of KX1 columns from the first column is X1, the weight of thenext KX2 columns is X2, the weight of the next KY1 columns is Y1, theweight of the next KY2 columns is Y2, the weight of the next M−1 columnsis 2, and the weight of the final column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=64800 bits)of the LGE code with (64k, 10/15).

The number of columns KX1, KX2, KY1, KY2, and M and the column weightsX1, X2, Y1, and Y2 in the parity check matrix H of the LGE code with(64k, 10/15) are set as illustrated in FIG. 79.

FIG. 80 is a diagram illustrating a parity check matrix H of a NERC codewith (64k, 9/15).

In the parity check matrix H of the NERC code with (64k, 9/15), theweight of KX1 columns from the first column is X1, the weight of thenext KX2 columns is X2, the weight of the next KY1 columns is Y1, theweight of the next KY2 columns is Y2, the weight of the next M−1 columnsis 2, and the weight of the final column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=64800 bits)of the NERC code with (64k, 9/15).

The number of columns KX1, KX2, KY1, KY2, and M and the column weightsX1, X2, Y1, and Y2 in the parity check matrix H of the NERC code with(64k, 9/15) are set as illustrated in FIG. 80.

FIG. 81 is a diagram illustrating a parity check matrix H of an ETRIcode with (16k, 5/15).

For the parity check matrix H of the ETRI code with (16k, 5/15), aparameter g=M₁ is 720.

Since the ETRI code with (16k, 5/15) has a code length N of 16200 and acoding rate r of 5/15, an information length K=N×r is 16200×5/15=5400and a parity length M=N−K is 16200−5400=10800.

In addition, a parameter M₂=M−M₁=N−K−g is 10800−720=10080.

Therefore, a parameter Q₁=M₁/P is 720/360=2 and a parameter Q₂=M₂/P is10080/360=28.

FIG. 82 is a diagram illustrating a parity check matrix H of ETRI codeswith (64k, 5/15), (64k, 6/15), and (64k, 7/15).

For the parity check matrix H of the ETRI codes with (64k, 5/15), (64k,6/15), and (64k, 7/15), the parameters g=M₁, M₂, Q₁, and Q₂ are asillustrated in FIG. 82.

<Constellation>

FIGS. 83 to 92 are diagrams illustrating an example of the type ofconstellation used in the transmission system illustrated in FIG. 7.

The transmission system illustrated in FIG. 7 can use constellationswhich are scheduled to be used in, for example, ATSC3.0.

In ATSC3.0, for MODCOD which is a combination of a modulation method andan LDPC code, constellations to be used in MODCOD are set.

Here, in ATSC3.0, five types of modulation methods, that is, QPSK,16QAM, 64QAM, 256QAM, and 1024QAM (1kQAM) are scheduled to be used.

In addition, in ATSC3.0, for two types of code lengths N of 16 k bitsand 64 k bits, LDPC codes with nine types of coding rates r of 5/15,6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15, that is, 18(=9×2) types of LDPC codes, are scheduled to be used.

In ATSC3.0, 18 types of LDPC codes are classified into nine typesaccording to the coding rate r (not according to the code length N) and45 (=9×5) combinations of nine types of LDPC codes (LDPC codes withcoding rates r or 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15,and 13/15) and five types of modulation methods are scheduled to be usedas MODCOD.

In ATSC 3.0, one or more constellations are scheduled to be used for oneMODCOD.

Examples of the constellation include a uniform constellation (UC) inwhich the arrangement of signal points is uniform and a non-uniformconstellation (NUC) in which the arrangement of signal points is notuniform.

Examples of the NUC include a constellation which is called a1-dimensional M²-QAM non-uniform constellation (1D NUC) and aconstellation which is called a 2-dimensional QQAM non-uniformconstellation (2D NUC).

In general, the 1D NUC has a higher BER than the UC, and the 2D NUC hasa higher BER than the 1D NUC.

The UC is used as the constellation of QPSK. In addition, for example,the 2D NUC is used as the constellations of 16QAM, 64QAM, and 256QAM.For example, the 1D NUC and the 2D NUC are used as the constellation of1024QAM.

Hereinafter, it is assumed that an NUC used in MODCOD in which themodulation method maps an m-bit symbol to any one of 2^(m) signal pointsand the coding rate of the LDPC code is r is referred to as NUC_2^(m)_r(here, m=2, 4, 6, 8, and 10).

For example, “NUC_16_6/15” indicates an NUC constellation used in MODCODin which the modulation method is 16QAM and the coding rate r of theLDPC code is 6/15.

In ATSC3.0, when the modulation method is QPSK, the same constellationis scheduled to be used for nine types of coding rates r of LDPC codes.

In ATSC3.0, when the modulation method is 16QAM, 64QAM, or 256QAM,different 2D NUC constellations are scheduled to be used for nine typesof coding rates r of LDPC codes.

In ATSC3.0, when the modulation method is 1024QAM, different 1D NUC and2D NUC constellations are scheduled to be used for nine types of codingrates r of LDPC codes.

Therefore, in ATSC3.0, one type of constellation is scheduled to beprepared for QPSK, nine types of 2D NUCs are scheduled to be preparedfor each of 16QAM, 64QAM, and 256QAM, and a total of 18 types ofconstellations, that is, nine types of 1D NUCs and nine types of 2DNUCs, are scheduled to be prepared for 1024QAM.

FIG. 83 is a diagram illustrating an example of constellations for ninetypes of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15,12, 15, and 13/15) of LDPC codes when the modulation method is 16QAM.

FIG. 84 is a diagram illustrating an example of constellations for ninetypes of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15,12, 15, and 13/15) of LDPC codes when the modulation method is 64QAM.

FIG. 85 is a diagram illustrating an example of constellations for eighttypes of coding rates r (=6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15,and 13/15) of LDPC codes when the modulation method is 256QAM.

FIG. 86 is a diagram illustrating an example of 1D NUC constellationsfor eight types of coding rates r (=6/15, 7/15, 8/15, 9/15, 10/15,11/15, 12, 15, and 13/15) of LDPC codes when the modulation method is1024QAM.

In FIGS. 83 to 86, the horizontal axis and the vertical axis indicate anI-axis and a Q-axis, respectively, and Re{x₁} and Im{x₁} indicate a realpart and an imaginary part of a signal point x₁ as the coordinates ofthe signal point x₁.

In FIGS. 83 to 86, numerical values which are described after “for CR”indicate the coding rates r of LDPC codes.

FIG. 87 is a diagram illustrating an example of the coordinates of asignal point of a common UC that is used for nine types of coding ratesr (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) ofLDPC codes when the modulation method is QPSK.

In FIG. 87, “Input cell word y” indicates a 2-bit symbol that is mappedto the UC of QPSK and “Constellation point z_(q)” indicates thecoordinates of a signal point z_(q). In addition, the index q of thesignal point z_(q) indicates the discrete time of the symbol (a timeinterval between a symbol and the next symbol).

In FIG. 87, the coordinates of the signal point z_(q) is represented inthe form of a complex number and i indicates an imaginary unit (√(−1)).

FIG. 88 is a diagram illustrating an example of the coordinates of asignal point of a 2D NUC that is used for nine types of coding rates r(=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPCcodes when the modulation method is 16QAM.

FIG. 89 is a diagram illustrating an example of the coordinates of asignal point of a 2D NUC that is used for nine types of coding rates r(=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPCcodes when the modulation method is 64QAM.

FIG. 90 is a diagram illustrating an example of the coordinates of asignal point of a 2D NUC that is used for eight types of coding rates r(=6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPC codeswhen the modulation method is 256QAM.

In FIGS. 88 to 90, NUC_2^(m)_r indicates the coordinates of a signalpoint of the 2D NUC when the modulation method is 2^(m)QAM and thecoding rate of the LDPC code is r.

In FIGS. 88 to 90, similarly to FIG. 87, the coordinates of a signalpoint z_(q) is represented in the form of a complex number and iindicates an imaginary unit.

In FIGS. 88 to 90, w#k indicates the coordinates of a signal point in afirst quadrant of a constellation.

In the 2D NUC, a signal point in a second quadrant of a constellation isarranged at the position that is obtained by symmetrically moving asignal point in the first quadrant with respect to the Q-axis and asignal point in a third quadrant of the constellation is arranged at theposition that is obtained by symmetrically moving a signal point in thefirst quadrant with respect to the origin. In addition, a signal pointin a fourth quadrant of the constellation is arranged at the positionthat is obtained by symmetrically moving a signal point in the firstquadrant with respect to the I-axis.

Here, when the modulation method is 2^(m)QAM, one m-bit symbol is mappedto a signal point corresponding to the symbol.

The m-bit symbol is represented by, for example, an integer of 0 to2^(m)-1. However, if b is 2^(m)/4, symbol y(0), y(1), . . . , y(2^(m)−1)which are represented by an integer of 0 to 2^(m)−1 can be classifiedinto four groups, that is, a group of symbols y(0) to y(b−1), a group ofsymbols y(b) to y(2b−1), a group of symbols y(2b) to y(3b−1), and agroup of symbols y(3b) to y(4b−1).

In FIGS. 88 to 90, a suffix k of w#k is an integer in the range of 0 tob-1 and w#k indicates the coordinates of a signal point corresponding toa symbol y(k) in the range of symbols y(0) to y(b−1).

The coordinates of a signal point corresponding to a symbol y(k+b) inthe range of symbols y(b) to y(2b−1) are represented by -conj(w#k) andthe coordinates of a signal point corresponding to a symbol y(k+2b) inthe range of symbols y(2b) to y(3b−1) are represented by conj(w#k). Inaddition, the coordinates of a signal point corresponding to a symboly(k+3b) in the range of symbols y(3b) to y(4b−1) are represented by−w#k.

Here, conj(w#k) indicates the complex conjugate of w#k.

For example, when the modulation method is 16QAM, “m” is 4 and “b” is 4(=2⁴/4). That is, 4-bit symbols y(0), y(1), . . . , y(15) are classifiedinto four groups of symbols y(0) to y(3), symbols y(4) to y(7), symbolsy(8) to y(11), and symbols y(12) to y(15).

Among the symbols y(0) to y(15), for example, the symbol y(12) is asymbol y(k+3b)=y(0+3×4) in the range of the symbols y(3b) to y(4b−1)(where k is 0). Therefore, the coordinates of a signal pointcorresponding to the symbol y(12) are −w#k=−w0.

As can be seen from FIG. 88, when the modulation method is 16QAM and thecoding rate r is 9/15 (NUC_16_9/15), w0 is 0.4967+1.1932i. Therefore,when the coding rate r of an LDPC code is, for example, 9/15, thecoordinates −w0 of a signal point corresponding to the symbol y(12) are−(0.4967+1.1932i).

FIG. 91 is a diagram illustrating an example of the coordinates of asignal point of a 1D NUC that is used for eight types of coding rates r(=6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPC codeswhen the modulation method is 1024QAM.

In FIG. 91, the column of NUC_1k_r indicates the value of u#k indicatingthe coordinates of a signal point of the 1D NUC that is used when themodulation method is 1024QAM and the coding rate of an LDPC code is r.

In addition, u#k indicates a real part Re(z_(q)) and an imaginary partIm(z_(q)) of a complex number as the coordinates of a signal point z_(q)of the 1D NUC.

FIG. 92 is a diagram illustrating the relationship between a symbol yand u#k indicating the real part Re(z_(q)) and the imaginary partIm(z_(q)) of a complex number as the coordinates of a signal point z_(q)of the 1D NUC corresponding to the symbol y.

It is assumed that a 10-bit symbol y of 1024QAM is represented byy_(0,q), y_(1,q), y_(2,q), y_(3,q), y_(4,q), y_(5,q), y_(6,q), y_(7,q),y_(8,q), and y_(9,q) from the first bit (most significant bit).

A of FIG. 92 illustrates a correspondence relationship between fiveodd-numbered bits y_(0,q), y_(2,q), y_(4,q), y_(6,q), y_(8,q) of thesymbol y and u#k indicating the rear part Re(z_(q)) of (the coordinatesof) the signal point z_(q) corresponding to the symbol y.

B of FIG. 92 illustrates a correspondence relationship between fiveeven-numbered bits y_(1,q), y_(3,q), y_(5,q), y_(7,q), y_(9,q) of thesymbol y and u#k indicating the imaginary part Im(z_(q)) of (thecoordinates of) the signal point z_(q) corresponding to the symbol y.

When a 10-bit symbol y=(y_(0,q), y_(1,q), y_(2,q), y_(3,q), y_(4,q),Y_(5,q), y_(6,q), Y_(7,q), y_(8,q), y_(9,q)) of 1024QAM is (0, 0, 1, 0,0, 1, 1, 1, 0, 0), five odd-numbered bits (y_(0,q), y_(2,q), y_(4,q),y_(6,q), y_(8,q)) are (0, 1, 0, 1, 0) and five even-numbered bits(y_(1,q), y_(3,q), y_(5,q), y_(7,q), y_(9,q)) are (0, 0, 1, 1, 0).

In A of FIG. 92, five odd-numbered bits (0, 1, 0, 1, 0) are associatedwith u3. Therefore, the rear part Re(z_(q)) of a signal point z_(q)corresponding to a symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u3.

In B of FIG. 92, five even-numbered bits (0, 0, 1, 1, 0) are associatedwith u11. Therefore, the imaginary part Im(z_(q)) of the signal pointz_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) isu11.

In contrast, as illustrated in FIG. 91, for 1D NUC (NUC_1k_7/15) that isused when the modulation method is 1024QAM and the coding rate r of anLDPC code is 7/15, when the coding rate r of an LDPC code is, forexample, 7/15, u3 is 1.04 and u11 is 6.28.

Therefore, the rear part Re(z_(q)) of the signal point z_(q)corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u3=1.04and the imaginary part Im(z_(q)) thereof is u11=6.28. As a result, thecoordinates of the signal point z_(q) corresponding to the symbol y=(0,0, 1, 0, 0, 1, 1, 1, 0, 0) are represented by 1.04+6.28i.

Signal points of the 1D NUC are arranged in a lattice shape on astraight line that is parallel to the I-axis or on a straight line thatis parallel to the Q-axis. The interval between the signal points is notuniform. In addition, in the transmission of (data mapped to) signalpoints, the average power of the signal points on a constellation isnormalized. When the mean square value of the absolute values of (thecoordinates of) all of the signal points of the constellation isrepresented by P_(ave), the normalization is performed by multiplyingeach signal point z_(q) on the constellation by the reciprocal1/(√P_(ave)) of the square root √P_(ave) of the mean square valueP_(ave).

The constellations described in FIGS. 83 to 92 show that a high errorrate is obtained.

<Block Interleaver 25>

FIG. 93 is a block diagram illustrating an example of the structure ofthe block interleaver 25 illustrated in FIG. 9.

The block interleaver 25 has a storage region which is called part 1 anda storage region which is called part 2.

Each of parts 1 and 2 includes C columns which are arranged in the rowdirection and of which the number is equal to the number of bits m of asymbol. Each of the columns functions as a storage region which storesone bit in the row (horizontal) direction and stores a predeterminednumber of bits in the column (vertical) direction.

When the number of bits which are stored in a column of part 1 in thecolumn direction (hereinafter, also referred to as a part column length)is represented by R1 and the part column length of a column of part 2 isrepresented by R2, (R1+R2)×C is equal to the code length N (64800 bitsor 16200 bits in this embodiment) of an LDPC code to be subjected toblock interleaving.

In addition, the part column length R1 is equal to a multiple of 360bits which is the unit size P and the part column length R2 is equal tothe remainder obtained when the sum R1+R2 (hereinafter, also referred toas a column length) of the part column length R1 of part 1 and the partcolumn length R2 of part 2 is divided by 360 bits which is the unit sizeP.

Here, the column length R1+R2 is equal to a value obtained by dividingthe code length N of the LDPC code to be subjected to block interleavingby the number of bits m of a symbol.

For example, when 16QAM is used as the modulation method for an LDPCcode having a code length N of 16200 bits, the column length R1+R2 is4050 (=16200/4) since the number of bits m of a symbol is 4 bits.

In addition, when the column length R1+R2=4050 is divided by 360 bitswhich is the unit size P, the remainder is 90. Therefore, the partcolumn length R2 of part 2 is 90 bits.

Therefore, the part column length R1 of part 1 is R1+R2−R2=4050−90 =3960bits.

FIG. 94 is a diagram illustrating the number of columns C of parts 1 and2 and the part column lengths (the number of rows) R1 and R2 withrespect to combinations of the code lengths N and the modulationmethods.

FIG. 94 illustrates the number of columns C of parts 1 and 2 and thepart column lengths R1 and R2 with respect to combinations of the LDPCcodes having code lengths N of 16200 bits and 64800 bits and themodulation methods QPSK, 16QAM, 64QAM, 256QAM, and 1024QAM.

FIG. 95 is a diagram illustrating block interleaving performed by theblock interleaver 25 illustrated in FIG. 93.

The block interleaver 25 writes and reads an LDPC code to and from parts1 and 2 to perform block interleaving.

That is, in block interleaving, as illustrated in A of FIG. 95, thewriting of the code bits of an LDPC code, which is one code word, fromthe top to the bottom of the columns in part 1 (in the column direction)is performed for the columns from the left to the right.

Then, when the writing of the code bits to the bottom of the rightmostcolumn (C-th column) among the columns in part 1 is completed, thewriting of the remaining code bits from the top to the bottom of thecolumns (column direction) in part 2 is performed for the columns fromthe left to the right.

Then, when the writing of the code bits to the bottom of the rightmostcolumn (C-th column) among the columns in part 2 is completed, code bitsare read from the first row of all of the C columns in part 1 in the rowdirection in units of C=m bits, as illustrated in B of FIG. 95.

Then, the reading of the code bits from all of the C columns in part 1is sequentially performed toward the lower rows. When the reading of thecode bits from an R1-th row, which is the final row, is completed, codebits are read from the first row of all of the C columns in part 2 inthe row direction in units of C=m bits.

The reading of the code bits from all of the C columns in part 2 issequentially performed toward the lower rows. The reading of the codebits is performed for an R2-th row which is the final row.

In this way, the code bits which are read from parts 1 and 2 in units ofm bits are supplied as symbols to the mapper 117 (FIG. 8).

<Group-Wise Interleaving>

FIG. 96 is a diagram illustrating group-wise interleaving performed bythe group-wise interleaver 24 illustrated in FIG. 9.

In group-wise interleaving, an LDPC code which is one code word isdivided into sections of 360 bits that is equal to the unit size P fromthe head of the LDPC code, one section of 360 bits is used as a bitgroup, and the LDPC code which is one code word is interleaved in unitsof bit groups according to a predetermined pattern (hereinafter, alsoreferred to as a GW pattern).

Hereinafter, when an LDPC code which is one code word is divided intobit groups from the head, an (i+1)-th bit group is referred to as a bitgroup i.

When the unit size P is 360, for example, an LDPC code with a codelength N of 1800 bits is divided into five (=1800/360) bit groups, thatis, bit groups 0, 1, 2, 3, and 4. In addition, an LDPC code with a codelength N of, for example, 16200 bits is sectioned to 45 (=16200/360) bitgroups, that is, bit groups 0, 1, . . . , 44. An LDPC code with a codelength N of 64800 bits is divided into 180 (=64800/360) bit groups, thatis, bit groups 0, 1, . . . , 179.

Hereinafter, the GW pattern is represented by a sequence of numbersindicating bit groups. For example, for the LDPC code with a code lengthN of 1800 bits, a GW pattern 4, 2, 0, 3, and 1 indicates interleaving(rearranging) a sequence of bit groups 0, 1, 2, 3, and 4 into a sequenceof bit groups 4, 2, 0, 3, and 1.

The GW pattern can be set at least for every code length N of LDPCcodes.

FIG. 97 is a diagram illustrating a first example of a GW pattern for anLDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 97, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

39, 47, 96, 176, 33, 75, 165, 38, 27, 58, 90, 76, 17, 46, 10, 91, 133,69, 171, 32, 117, 78, 13, 146, 101, 36, 0, 138, 25, 77, 122, 49, 14,125, 140, 93, 130, 2, 104, 102, 128, 4, 111, 151, 84, 167, 35, 127, 156,55, 82, 85, 66, 114, 8, 147, 115, 113, 5, 31, 100, 106, 48, 52, 67, 107,18, 126, 112, 50, 9, 143, 28, 160, 71, 79, 43, 98, 86, 94, 64, 3, 166,105, 103, 118, 63, 51, 139, 172, 141, 175, 56, 74, 95, 29, 45, 129, 120,168, 92, 150, 7, 162, 153, 137, 108, 159, 157, 173, 23, 89, 132, 57, 37,70, 134, 40, 21, 149, 80, 1, 121, 59, 110, 142, 152, 15, 154, 145, 12,170, 54, 155, 99, 22, 123, 72, 177, 131, 116, 44, 158, 73, 11, 65, 164,119, 174, 34, 83, 53, 24, 42, 60, 26, 161, 68, 178, 41, 148, 109, 87,144, 135, 20, 62, 81, 169, 124, 6, 19, 30, 163, 61, 179, 136, 97, 16, 88

FIG. 98 is a diagram illustrating a second example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 98, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

6, 14, 1, 127, 161, 177, 75, 123, 62, 103, 17, 18, 167, 88, 27, 34, 8,110, 7, 78, 94, 44, 45, 166, 149, 61, 163, 145, 155, 157, 82, 130, 70,92, 151, 139, 160, 133, 26, 2, 79, 15, 95, 122, 126, 178, 101, 24, 138,146, 179, 30, 86, 58, 11, 121, 159, 49, 84, 132, 117, 119, 50, 52, 4,51, 48, 74, 114, 59, 40, 131, 33, 89, 66, 136, 72, 16, 134, 37, 164, 77,99, 173, 20, 158, 156, 90, 41, 176, 81, 42, 60, 109, 22, 150, 105, 120,12, 64, 56, 68, 111, 21, 148, 53, 169, 97, 108, 35, 140, 91, 115, 152,36, 106, 154, 0, 25, 54, 63, 172, 80, 168, 142, 118, 162, 135, 73, 83,153, 141, 9, 28, 55, 31, 112, 107, 85, 100, 175, 23, 57, 47, 38, 170,137, 76, 147, 93, 19, 98, 124, 39, 87, 174, 144, 46, 10, 129, 69, 71,125, 96, 116, 171, 128, 65, 102, 5, 43, 143, 104, 13, 67, 29, 3, 113,32, 165

FIG. 99 is a diagram illustrating a third example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 99, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

103, 116, 158, 0, 27, 73, 140, 30, 148, 36, 153, 154, 10, 174, 122, 178,6, 106, 162, 59, 142, 112, 7, 74, 11, 51, 49, 72, 31, 65, 156, 95, 171,105, 173, 168, 1, 155, 125, 82, 86, 161, 57, 165, 54, 26, 121, 25, 157,93, 22, 34, 33, 39, 19, 46, 150, 141, 12, 9, 79, 118, 24, 17, 85, 117,67, 58, 129, 160, 89, 61, 146, 77, 130, 102, 101, 137, 94, 69, 14, 133,60, 149, 136, 16, 108, 41, 90, 28, 144, 13, 175, 114, 2, 18, 63, 68, 21,109, 53, 123, 75, 81, 143, 169, 42, 119, 138, 104, 4, 131, 145, 8, 5,76, 15, 88, 177, 124, 45, 97, 64, 100, 37, 132, 38, 44, 107, 35, 43, 80,50, 91, 152, 78, 166, 55, 115, 170, 159, 147, 167, 87, 83, 29, 96, 172,48, 98, 62, 139, 70, 164, 84, 47, 151, 134, 126, 113, 179, 110, 111,128, 32, 52, 66, 40, 135, 176, 99, 127, 163, 3, 120, 71, 56, 92, 23, 20

FIG. 100 is a diagram illustrating a fourth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 100, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

139, 106, 125, 81, 88, 104, 3, 66, 60, 65, 2, 95, 155, 24, 151, 5, 51,53, 29, 75, 52, 85, 8, 22, 98, 93, 168, 15, 86, 126, 173, 100, 130, 176,20, 10, 87, 92, 175, 36, 143, 110, 67, 146, 149, 127, 133, 42, 84, 64,78, 1, 48, 159, 79, 138, 46, 112, 164, 31, 152, 57, 144, 69, 27, 136,122, 170, 132, 171, 129, 115, 107, 134, 89, 157, 113, 119, 135, 45, 148,83, 114, 71, 128, 161, 140, 26, 13, 59, 38, 35, 96, 28, 0, 80, 174, 137,49, 16, 101, 74, 179, 91, 44, 55, 169, 131, 163, 123, 145, 162, 108,178, 12, 77, 167, 21, 154, 82, 54, 90, 177, 17, 41, 39, 7, 102, 156, 62,109, 14, 37, 23, 153, 6, 147, 50, 47, 63, 18, 70, 68, 124, 72, 33, 158,32, 118, 99, 105, 94, 25, 121, 166, 120, 160, 141, 165, 111, 19, 150,97, 76, 73, 142, 117, 4, 172, 58, 11, 30, 9, 103, 40, 61, 43, 34, 56,116

FIG. 101 is a diagram illustrating a fifth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 101, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

72, 59, 65, 61, 80, 2, 66, 23, 69, 101, 19, 16, 53, 109, 74, 106, 113,56, 97, 30, 164, 15, 25, 20, 117, 76, 50, 82, 178, 13, 169, 36, 107, 40,122, 138, 42, 96, 27, 163, 46, 64, 124, 57, 87, 120, 168, 166, 39, 177,22, 67, 134, 9, 102, 28, 148, 91, 83, 88, 167, 32, 99, 140, 60, 152, 1,123, 29, 154, 26, 70, 149, 171, 12, 6, 55, 100, 62, 86, 114, 174, 132,139, 7, 45, 103, 130, 31, 49, 151, 119, 79, 41, 118, 126, 3, 179, 110,111, 51, 93, 145, 73, 133, 54, 104, 161, 37, 129, 63, 38, 95, 159, 89,112, 115, 136, 33, 68, 17, 35, 137, 173, 143, 78, 77, 141, 150, 58, 158,125, 156, 24, 105, 98, 43, 84, 92, 128, 165, 153, 108, 0, 121, 170, 131,144, 47, 157, 11, 155, 176, 48, 135, 4, 116, 146, 127, 52, 162, 142, 8,5, 34, 85, 90, 44, 172, 94, 160, 175, 75, 71, 18, 147, 10, 21, 14, 81

FIG. 102 is a diagram illustrating a sixth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 102, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

8, 27, 7, 70, 75, 84, 50, 131, 146, 99, 96, 141, 155, 157, 82, 57, 120,38, 137, 13, 83, 23, 40, 9, 56, 171, 124, 172, 39, 142, 20, 128, 133, 2,89, 153, 103, 112, 129, 151, 162, 106, 14, 62, 107, 110, 73, 71, 177,154, 80, 176, 24, 91, 32, 173, 25, 16, 17, 159, 21, 92, 6, 67, 81, 37,15, 136, 100, 64, 102, 163, 168, 18, 78, 76, 45, 140, 123, 118, 58, 122,11, 19, 86, 98, 119, 111, 26, 138, 125, 74, 97, 63, 10, 152, 161, 175,87, 52, 60, 22, 79, 104, 30, 158, 54, 145, 49, 34, 166, 109, 179, 174,93, 41, 116, 48, 3, 29, 134, 167, 105, 132, 114, 169, 147, 144, 77, 61,170, 90, 178, 0, 43, 149, 130, 117, 47, 44, 36, 115, 88, 101, 148, 69,46, 94, 143, 164, 139, 126, 160, 156, 33, 113, 65, 121, 53, 42, 66, 165,85, 127, 135, 5, 55, 150, 72, 35, 31, 51, 4, 1, 68, 12, 28, 95, 59, 108

FIG. 103 is a diagram illustrating a seventh example of the GW patternfor the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 103, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36,38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72,74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106,108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17,19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53,55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89,91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119,121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147,149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175,177, 179

FIG. 104 is a diagram illustrating an eighth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 104, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

11, 5, 8, 18, 1, 25, 32, 31, 19, 21, 50, 102, 65, 85, 45, 86, 98, 104,64, 78, 72, 53, 103, 79, 93, 41, 82, 108, 112, 116, 120, 124, 128, 132,136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 4, 12, 15, 3, 10,20, 26, 34, 23, 33, 68, 63, 69, 92, 44, 90, 75, 56, 100, 47, 106, 42,39, 97, 99, 89, 52, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145,149, 153, 157, 161, 165, 169, 173, 177, 6, 16, 14, 7, 13, 36, 28, 29,37, 73, 70, 54, 76, 91, 66, 80, 88, 51, 96, 81, 95, 38, 57, 105, 107,59, 61, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158,162, 166, 170, 174, 178, 0, 9, 17, 2, 27, 30, 24, 22, 35, 77, 74, 46,94, 62, 87, 83, 101, 49, 43, 84, 48, 60, 67, 71, 58, 40, 55, 111, 115,119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171,175, 179

FIG. 105 is a diagram illustrating a ninth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 105, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

9, 18, 15, 13, 35, 26, 28, 99, 40, 68, 85, 58, 63, 104, 50, 52, 94, 69,108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 8, 16, 17,24, 37, 23, 22, 103, 64, 43, 47, 56, 92, 59, 70, 42, 106, 60, 109, 115,121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 4, 1, 10, 19, 30, 31,89, 86, 77, 81, 51, 79, 83, 48, 45, 62, 67, 65, 110, 116, 122, 128, 134,140, 146, 152, 158, 164, 170, 176, 6, 2, 0, 25, 20, 34, 98, 105, 82, 96,90, 107, 53, 74, 73, 93, 55, 102, 111, 117, 123, 129, 135, 141, 147,153, 159, 165, 171, 177, 14, 7, 3, 27, 21, 33, 44, 97, 38, 75, 72, 41,84, 80, 100, 87, 76, 57, 112, 118, 124, 130, 136, 142, 148, 154, 160,166, 172, 178, 5, 11, 12, 32, 29, 36, 88, 71, 78, 95, 49, 54, 61, 66,46, 39, 101, 91, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173,179

FIG. 106 is a diagram illustrating a tenth example of the GW pattern forthe LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 106, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107,31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129,52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97,33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17,15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130,56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45,78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96,32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149,151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177,179

FIG. 107 is a diagram illustrating an eleventh example of the GW patternfor the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 107, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73,100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114,132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10,13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95,86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141,145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82,32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70,91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158,162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131,33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60,67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175,179

FIG. 108 is a diagram illustrating a twelfth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 108, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72,116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9,5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55,103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28,104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125,58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101,94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135,141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47,80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148,154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42,114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161,167, 173, 179

FIG. 109 is a diagram illustrating a thirteenth example of the GWpattern for the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 109, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36,38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72,74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106,108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134,136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162,164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17,19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53,55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89,91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119,121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147,149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175,177, 179

FIG. 110 is a diagram illustrating a fourteenth example of the GWpattern for the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 110, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups. 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108,112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164,168, 172, 176, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57,61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121,125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2,6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74,78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134,138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 3, 7, 11, 15, 19,23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91,95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151,155, 159, 163, 167, 171, 175, 179

FIG. 111 is a diagram illustrating a fifteenth example of the GW patternfor the LDPC code with a code length N of 64 kbits.

According to the GW pattern illustrated in FIG. 111, a sequence of bitgroups 0 to 179 of the 64-kbit LDPC code is interleaved into a sequenceof the following bit groups.

8, 112, 92, 165, 12, 55, 5, 126, 87, 70, 69, 94, 103, 78, 137, 148, 9,60, 13, 7, 178, 79, 43, 136, 34, 68, 118, 152, 49, 15, 99, 61, 66, 28,109, 125, 33, 167, 81, 93, 97, 26, 35, 30, 153, 131, 122, 71, 107, 130,76, 4, 95, 42, 58, 134, 0, 89, 75, 40, 129, 31, 80, 101, 52, 16, 142,44, 138, 46, 116, 27, 82, 88, 143, 128, 72, 29, 83, 117, 172, 14, 51,159, 48, 160, 100, 1, 102, 90, 22, 3, 114, 19, 108, 113, 39, 73, 111,155, 106, 105, 91, 150, 54, 25, 135, 139, 147, 36, 56, 123, 6, 67, 104,96, 157, 10, 62, 164, 86, 74, 133, 120, 174, 53, 140, 156, 171, 149,127, 85, 59, 124, 84, 11, 21, 132, 41, 145, 158, 32, 17, 23, 50, 169,170, 38, 18, 151, 24, 166, 175, 2, 47, 57, 98, 20, 177, 161, 154, 176,163, 37, 110, 168, 141, 64, 65, 173, 162, 121, 45, 77, 115, 179, 63,119, 146, 144

The first to fifteenth examples of the GW pattern for the LDPC code witha code length N of 64 kbits can also be applied to any combination of anLDPC code with a code length N of 64 kbits and an arbitrary coding rater and an arbitrary modulation method (constellation).

However, for group-wise interleaving, a GW pattern to be applied can beset for each combination of the code length N of an LDPC code, thecoding rate r of an LDPC code, and a modulation method (constellation).In this case, it is possible to further reduce an error rate for eachcombination.

In particular, the GW pattern illustrated in FIG. 97 can be applied to,for example, a combination of the ETRI code with (64 k, 5/15) and QPSKto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 98 can be applied to,for example, a combination of the ETRI code with (64 k, 5/15) and 16QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 99 can be applied to,for example, a combination of the ETRI code with (64 k, 5/15) and 64QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 100 can be applied to,for example, a combination of the Sony code with (64 k, 7/15) and QPSKto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 101 can be applied to,for example, a combination of the

Sony code with (64 k, 7/15) and 16QAM to achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 102 can be applied to,for example, a combination of the Sony code with (64 k, 7/15) and 64QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 103 can be applied to,for example, a combination of the Sony code with (64 k, 9/15) and QPSKto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 104 can be applied to,for example, a combination of the Sony code with (64 k, 9/15) and 16QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 105 can be applied to,for example, a combination of the Sony code with (64 k, 9/15) and 64QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 106 can be applied to,for example, a combination of the Sony code with (64 k, 11/15) and QPSKto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 107 can be applied to,for example, a combination of the Sony code with (64 k, 11/15) and 16QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 108 can be applied to,for example, a combination of the Sony code with (64 k, 11/15) and 64QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 109 can be applied to,for example, a combination of the Sony code with (64 k, 13/15) and QPSKto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 110 can be applied to,for example, a combination of the Sony code with (64 k, 13/15) and 16QAMto achieve a low error rate.

In particular, the GW pattern illustrated in FIG. 111 can be applied to,for example, a combination of the Sony code with (64 k, 13/15) and 64QAMto achieve a low error rate.

FIG. 112 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 97 is applied to a combination of the ETRI code with (64k, 5/15)and QPSK.

FIG. 113 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 98 is applied to a combination of the ETRI code with (64k, 5/15)and 16QAM.

FIG. 114 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 99 is applied to a combination of the ETRI code with (64k, 5/15)and 64QAM.

FIG. 115 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 100 is applied to a combination of the Sony code with (64k,7/15) and QPSK.

FIG. 116 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 101 is applied to a combination of the Sony code with (64k,7/15) and 16QAM.

FIG. 117 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 102 is applied to a combination of the Sony code with (64k,7/15) and 64QAM.

FIG. 118 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 103 is applied to a combination of the Sony code with (64k,9/15) and QPSK.

FIG. 119 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 104 is applied to a combination of the Sony code with (64k,9/15) and 16QAM.

FIG. 120 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 105 is applied to a combination of the Sony code with (64k,9/15) and 64QAM.

FIG. 121 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 106 is applied to a combination of the Sony code with (64k,11/15) and QPSK.

FIG. 122 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 107 is applied to a combination of the Sony code with (64k,11/15) and 16QAM.

FIG. 123 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 108 is applied to a combination of the Sony code with (64k,11/15) and 64QAM.

FIG. 124 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 109 is applied to a combination of the Sony code with (64k,13/15) and QPSK.

FIG. 125 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 110 is applied to a combination of the Sony code with (64k,13/15) and 16QAM.

FIG. 126 is a diagram illustrating a BER/FER curve as the result of asimulation which measures an error rate when the GW pattern illustratedin FIG. 111 is applied to a combination of the Sony code with (64k,13/15) and 64QAM.

FIGS. 112 to 126 illustrate BER/FER curves when an AWGN channel is usedas the communication path 13 (FIG. 7) (upper graphs) and when a Rayleigh(fading) channel is used as the communication path 13 (lower graphs).

In FIGS. 112 to 126, solid lines (w bil) indicate BER/FER curves whenparity interleaving, group-wise interleaving, and block-wiseinterleaving are performed and dotted lines (w/o bil) indicate BER/FERcurves when parity interleaving, group-wise interleaving, and block-wiseinterleaving are not performed.

As can be seen from FIGS. 112 to 126, when parity interleaving,group-wise interleaving, and block-wise interleaving are performed, itis possible to improve BER/FER and to achieve a low error rate, ascompared to a case in which parity interleaving, group-wiseinterleaving, and block-wise interleaving are not performed.

The GW patterns illustrated in FIGS. 97 to 111 can be applied to, forexample, constellations obtained by symmetrically moving the signalpoint constellations illustrated in FIGS. 87 to 89 with respect to theI-axis or the Q-axis, constellations obtained by symmetrically movingthe signal point constellations with respect to the origin, andconstellations obtained by rotating the signal point constellationsabout the origin by an arbitrary angle, in addition to the signal pointconstellations of QPSK, 16QAM, and 64QAM illustrated in FIGS. 87 to 89.In this case, it is possible to obtain the same effect as that when theGW patterns are applied to the signal point constellations of QPSK,16QAM, and 64QAM illustrated in FIGS. 87 to 89.

In addition, the GW patterns illustrated in FIGS. 97 to 111 can beapplied to, for example, constellations obtained by interchanging themost significant bit (MSB) and the least significant bit (LSB) of thesymbols corresponding (allocated) to the signal points in the signalpoint constellations illustrated in FIGS. 87 to 89, in addition to thesignal point constellations of QPSK, 16QAM, and 64QAM illustrated inFIGS. 87 to 89. In this case, it is possible to obtain the same effectas that when the GW patterns are applied to the signal pointconstellations of QPSK, 16QAM, and 64QAM illustrated in FIGS. 87 to 89.

<Example of Structure of Receiving Device 12>

FIG. 127 is a block diagram illustrating an example of the structure ofthe receiving device 12 illustrated in FIG. 7.

An OFDM processing (OFDM operation) unit 151 receives an OFDM signalfrom the transmitting device 11 (FIG. 7) and performs signal processingfor the OFDM signal. Data which is obtained by the signal processing ofthe OFDM processing unit 151 is supplied to a frame management unit 152.

The frame management unit 152 processes (interprets) a frame which isformed by the data supplied from the OFDM processing unit 151 andsupplies a target data signal obtained by the processing and a controldata signal to frequency deinterleavers 161 and 153.

The frequency deinterleaver 153 performs frequency deinterleaving forthe data from the frame management unit 152 in units of symbols andsupplies the data to a demapper 154.

The demapper 154 performs demapping (signal point constellationdecoding) for the data (data on the constellation) transmitted from thefrequency deinterleaver 153, on the basis of the signal pointconstellation which is determined by the quadrature modulation performedby the transmitting device 11, to perform quadrature demodulation andsupplies data obtained by the quadrature demodulation ((the likelihoodof) the LDPC code) to an LDPC decoder 155.

The LDPC decoder 155 decodes the LDPC code from the demapper 154 andsupplies LDPC target data (here, a BCH code) obtained by the decoding toa BCH decoder 156.

The BCH decoder 156 performs BCH decoding for the LDPC target data fromthe LDPC decoder 155 and outputs control data (signaling) obtained bythe BCH decoding.

The frequency deinterleaver 161 performs frequency deinterleaving forthe data from the frame management unit 152 in units of symbols andsupplies the data to a SISO/MISO decoder 162.

The SISO/MISO decoder 162 performs spatiotemporal decoding for the datatransmitted from the frequency deinterleaver 161 and supplies the datato a time deinterleaver 163.

The time deinterleaver 163 performs time deinterleaving for the datatransmitted from the SISO/MISO decoder 162 in units of symbols andsupplies the data to a demapper 164.

The demapper 164 performs demapping (signal point constellationdecoding) for the data (data on the constellation) transmitted from thetime deinterleaver 163, on the basis of the signal point constellationwhich is determined by the quadrature modulation performed by thetransmitting device 11, to perform quadrature demodulation and suppliesdata obtained by the quadrature demodulation to a bit deinterleaver 165.

The bit deinterleaver 165 performs bit deinterleaving for the datatransmitted from the demapper 164 and supplies (the likelihood of) anLDPC code, which is bit-interleaved data, to an LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding for the LDPC codetransmitted from the bit deinterleaver 165 and supplies LDPC target data(here, a BCH code) obtained by the LDPC decoding to a BCH decoder 167.

The BCH decoder 167 performs BCH decoding for the LDPC target datatransmitted from the LDPC decoder 155 and supplies data obtained by theBCH decoding to a BB descrambler 168.

The BB descrambler 168 performs BB descrambling for the data transmittedfrom the BCH decoder 167 and supplies data obtained by the BBdescrambling to a null deletion unit 169.

The null deletion unit 169 deletes null data inserted by the padder 112illustrated in FIG. 8 from the data transmitted from the BB descrambler168 and supplies the data to a demultiplexer 170.

The demultiplexer 170 separates one or more streams (target data) whichare multiplexed into the data from the null deletion unit 169, performsnecessary processing, and outputs the target data as output streams.

The receiving device 12 can be configured without some of the blocksillustrated in FIG. 127. That is, for example, when the transmittingdevice 11 (FIG. 8) is configured without the time interleaver 118, theSISO/MISO encoder 119, the frequency interleaver 120, and the frequencyinterleaver 124, the receiving device 12 can be configured without thetime deinterleaver 163, the SISO/MISO decoder 162, the frequencydeinterleaver 161, and the frequency deinterleaver 153 which are blockscorresponding to the time interleaver 118, the SISO/MISO encoder 119,the frequency interleaver 120, and the frequency interleaver 124 of thetransmitting device 11, respectively.

<Example of Structure of Bit Deinterleaver 165>

FIG. 128 is a block diagram illustrating an example of the structure ofthe bit deinterleaver 165 illustrated in FIG. 127.

The bit deinterleaver 165 includes a block deinterleaver 54 and agroup-wise deinterleaver 55 and performs (bit) deinterleaving for thesymbol bits of symbols which are data from the demapper 164 (FIG. 127).

That is, the block deinterleaver 54 performs block deinterleaving (aninverse process of block interleaving) corresponding to the blockinterleaving which is performed by the block interleaver 25 illustratedin FIG. 9, that is, block deinterleaving which returns the positions of(the likelihood of) the code bits of the LDPC code rearranged by theblock interleaving to the original positions, for the symbol bits of thesymbols transmitted from the demapper 164 and supplies the LDPC codeobtained by the block deinterleaving to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleaving (aninverse process of group-wise interleaving) corresponding to thegroup-wise interleaving which is performed by the group-wise interleaver24 illustrated in FIG. 9, that is, group-wise deinterleaving thatreturns the sequences of the code bits of the LDPC code, which arechanged in units of bit groups by the group-wise interleaving describedin FIG. 96, to the original sequences, for the LDPC code transmittedfrom the block deinterleaver 54, by rearranging the code bits in unitsof bit groups.

Here, when parity interleaving, group-wise interleaving, and blockinterleaving are performed for the LDPC code which is supplied from thedemapper 164 to the bit deinterleaver 165, the bit deinterleaver 165 canperform all of parity deinterleaving corresponding to the parityinterleaving (an inverse process of the parity interleaving, that is,parity deinterleaving which returns the sequence of the code bits of theLDPC code changed by the parity interleaving to the original sequence),block deinterleaving corresponding to the block interleaving, andgroup-wise deinterleaving corresponding to the group-wise interleaving.

In the bit deinterleaver 165 illustrated in FIG. 128, the blockdeinterleaver 54 which performs block deinterleaving corresponding tothe block interleaving and the group-wise deinterleaver 55 whichperforms group-wise deinterleaving corresponding to the group-wiseinterleaving are provided. However, a block which performs paritydeinterleaving corresponding to the parity interleaving is not provided.Therefore, parity deinterleaving is not performed.

Therefore, the LDPC code which has been subjected to blockdeinterleaving and group-wise deinterleaving, but has not been subjectedto parity deinterleaving is supplied from (the group-wise deinterleaver55 of) the bit deinterleaver 165 to the LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding for the LDPC codetransmitted from the bit deinterleaver 165, using a transformed paritycheck matrix obtained by performing at least column permutationcorresponding to parity interleaving for the parity check matrix H basedon the DVB method which is used for LDPC coding by the LDPC encoder 115illustrated in FIG. 8 (or the transformed parity check matrix (FIG. 29)obtained by performing row permutation for the parity check matrix (FIG.27) based on the ETRI method), and outputs data obtained by the LDPCdecoding as the decoding result of the LDPC target data.

FIG. 129 is a flowchart illustrating the process performed by thedemapper 164, the bit deinterleaver 165, and the LDPC decoder 166illustrated in FIG. 128.

In Step S111, the demapper 164 demaps the data from the timedeinterleaver 163 (data on the constellation which is mapped to signalpoints) to perform quadrature demodulation and supplies the data to thebit deinterleaver 165. Then, the process proceeds to Step S112.

In Step S112, the bit deinterleaver 165 performs deinterleaving (bitdeinterleaving) for the data from the demapper 164. Then, the processproceeds to Step S113.

That is, in Step S112, in the bit deinterleaver 165, the blockdeinterleaver 54 performs block deinterleaving for the data (symbols)from the demapper 164 and supplies the code bits of the LDPC codeobtained by the block deinterleaving to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleaving forthe LDPC code from the block deinterleaver 54 and supplies (thelikelihood of) the LDPC code obtained by the group-wise deinterleavingto the LDPC decoder 166.

In Step S113, the LDPC decoder 166 performs LDPC decoding for the LDPCcode from the group-wise deinterleaver 55, using the parity check matrixH which is used for LDPC coding by the LDPC encoder 115 illustrated inFIG. 8, that is, using, for example, the transformed parity check matrixobtained from the parity check matrix H, and outputs data obtained bythe LDPC decoding to the BCH decoder 167 as the decoding result of theLDPC target data.

In FIG. 128, similarly to FIG. 9, for simplicity of explanation, theblock deinterleaver 54 which performs block deinterleaving and thegroup-wise deinterleaver 55 which performs group-wise deinterleaving areseparately provided. However, the block deinterleaver 54 and thegroup-wise deinterleaver 55 may be integrally provided.

<LDPC Decoding>

The LDPC decoding performed by the LDPC decoder 166 illustrated in FIG.127 will be further described.

As described above, the LDPC decoder 166 illustrated in FIG. 127performs LDPC decoding for the LDPC code from the group-wisedeinterleaver 55, which has been subjected to block deinterleaving andgroup-wise deinterleaving, but has not been subjected to paritydeinterleaving, using the transformed parity check matrix obtained byperforming at least column permutation corresponding to parityinterleaving for the parity check matrix H based on the DVB method whichis used for LDPC coding by the LDPC encoder 115 illustrated in FIG. 8(or the transformed parity check matrix (FIG. 29) obtained by performingrow permutation for the parity check matrix (FIG. 27) based on the ETRImethod).

Here, LDPC decoding has been proposed which is performed using atransformed parity check matrix and can maintain an operation frequencyin a sufficiently feasible range while preventing an increase in acircuit size (for example, see Japanese Patent No. 4224777).

First, the LDPC decoding using the transformed parity check matrix whichhas been proposed will be described with reference to FIGS. 130 to 133.

FIG. 130 is a diagram illustrating an example of a parity check matrix Hof an LDPC code with a code length N of 90 and a coding rate of 2/3.

In FIG. 130, 0 is represented by a period (.) (which holds for FIGS. 131and 132).

In the parity check matrix H illustrated in FIG. 130, a parity matrixhas a dual diagonal structure.

FIG. 131 is a diagram illustrating a parity check matrix H′ which isobtained by performing row permutation represented by Formula (11) andcolumn permutation represented by Formula (12) for the parity checkmatrix H illustrated in FIG. 130.

Row permutation: a (6s+t+1)-th row→a (5t+s+1)-th row   (11)

Column permutation: a (6x+y+61)-th column→a (5y+x+61)-th column   (12)

In Formulas (11) and (12), s, t, x, and y are integers in the ranges of0≤s<5, 0≤t<6, 0≤x<5, and 0≤t<6, respectively.

According to the row permutation represented by Formula (11), the 1st,7th, 13th, 19th, and 25th rows which have the remainder of 1 when theirnumbers are divided by 6 are substituted with the 1st, 2nd, 3rd, 4th,and 5th rows and the 2nd, 8th, 14th, 20th, and 26th rows which have theremainder of 2 when their numbers are divided by 6 are substituted withthe 6th, 7th, 8th, 9th, and 10th rows.

According to the column permutation represented by Formula (12), forcolumns after a 61st column (parity matrix), the 61st, 67th, 73rd, 79th,and 85th columns which have the remainder of 1 when their numbers aredivided by 6 are substituted with the 61st, 62nd, 63rd, 64th, and 65thcolumns and the 62nd, 68th, 74th, 80th, and 86th columns have theremainder of 2 when their numbers are divided by 6 are substituted withthe 66th, 67th, 68th, 69th, and 70th columns.

In this way, a matrix which is obtained by performing row permutationand column permutation for the parity check matrix H illustrated in FIG.130 is the parity check matrix H′ illustrated in FIG. 131.

Here, even when row permutation is performed for the parity check matrixH, the sequence of the code bits of the LDPC code is not affected by therow permutation.

addition, the column permutation represented by

Formula (12) corresponds to parity interleaving which interleaves a(K+qx+y+1)-th code bit into the position of a (K+Py+x+1)-th code bitwhen an information length K is 60, the unit size P is 5, and a divisorq (=M/P) of a parity length M (here, 30) is 6.

Therefore, the parity check matrix H′ illustrated in FIG. 131 is atransformed parity check matrix obtained by performing at least columnpermutation which substitutes the (K+qx+y+1)-th column with the(K+Py+x+1)-th column in the parity check matrix (hereinafter,appropriately referred to as the original parity check matrix) Hillustrated in FIG. 130.

When the parity check matrix H′ illustrated in FIG. 131 is multiplied bya matrix that is obtained by performing the same permutation as thatrepresented by Formula (12) for the LDPC code with the original paritycheck matrix H illustrated in FIG. 130, a zero vector is output. Thatis, when a row vector that is obtained by performing the columnpermutation represented by Formula (12) for a row vector c serving asthe LDPC code (one code word) with the original parity check matrix H isrepresented by c′, Hc^(T) becomes a zero vector from the properties ofthe parity check matrix. Therefore, H′c′^(T) is also a zero vector.

Based on the above, the parity check matrix H′ illustrated in FIG. 131is a parity check matrix of the LDPC code c′ obtained by performing thecolumn permutation represented by Formula (12) for the LDPC code c withthe original parity check matrix H.

As described above, the column permutation represented by Formula (12)is performed for the LDPC code c with the original parity check matrixH, the LDPC code c′ subjected to the column permutation is decoded(LDPC-decoded), using the transformed parity check matrix H′ illustratedin FIG. 131, and permutation reverse to the column permutationrepresented by Formula (12) is performed for the decoding result.Therefore, it is possible to obtain the same decoding result as thatobtained when the LDPC code with the original parity check matrix H isdecoded using the parity check matrix H.

FIG. 132 is a diagram illustrating the transformed parity check matrixH′ illustrated in FIG. 131 which has 5×5 unit matrices.

In FIG. 132, the transformed parity check matrix H′ is represented by acombination of a 5×5 (=P×P) unit matrix, a matrix (hereinafter,appropriately referred to as a quasi unit matrix) obtained bysubstituting one or more is in the unit matrix with 0, a matrix(hereinafter, appropriately referred to as a shifted matrix) obtained bycyclically shifting the unit matrix or the quasi unit matrix, the sum(hereinafter, appropriately referred to as a sum matrix) of two or moreof the unit matrix, the quasi unit matrix, and the shifted matrix, and a5×5 zero matrix.

It can be said that the transformed parity check matrix H′ illustratedin FIG. 132 is formed by 5×5 unit matrices, quasi unit matrices, shiftedmatrices, sum matrices, and zero matrices. Therefore, hereinafter, the5×5 matrices (the unit matrix, the quasi unit matrix, the shiftedmatrix, the sum matrix, and the zero matrix) that form the transformedparity check matrix H′ are appropriately referred to as constitutivematrices.

An architecture in which check node operations and variable nodeoperations are simultaneously performed P times can be used to decode anLDPC code with a parity check matrix represented by P×P constitutivematrices.

FIG. 133 is a block diagram illustrating an example of the structure ofa decoding device which decodes the LDPC code.

That is, FIG. 133 illustrates an example of the structure of thedecoding device that decodes an LDPC code using the transformed paritycheck matrix H′ illustrated in FIG. 132 which is obtained by performingat least the column permutation represented by Formula (12) for theoriginal parity check matrix H illustrated in FIG. 130.

The decoding device illustrated in FIG. 133 includes an edge datastorage memory 300 including six FIFOs 300 ₁ to 300 ₆, a selector 301that selects one of the FIFOs 300 ₁ to 300 ₆, a check node calculationunit 302, two cyclic shift circuits 303 and 308, an edge data storagememory 304 including 18 FIFOs 304 ₁ to 304 ₁₈, a selector 305 thatselects one of the FIFOs 304 ₁ to 304 ₁₈, a received data memory 306that stores received data, a variable node calculation unit 307, adecoding word calculation unit 309, a received data rearrangement unit310, and a decoded data rearrangement unit 311.

First, a method for storing data in the edge data storage memories 300and 304 will be described.

The edge data storage memory 300 includes six FIFOs 300 ₁ to 300 ₆ ofwhich the number is equal to a value obtained by dividing the number ofrows 30 in the transformed parity check matrix H′ illustrated in FIG.132 by the number of rows 5 (the unit size P) in the constitutivematrix. A FIFO 300 _(y) (y=1, 2, . . . , 6) includes storage regions ina plurality of stages. Messages corresponding to five edges, of whichthe number is equal to the number of rows and the number of columns (theunit size P) in the constitutive matrix, can be simultaneously read andwritten from and to the storage region in each stage. The number ofstages of the storage regions in the FIFO 300 _(y) is 9 that is themaximum number of 1s (Hamming weight) of the row direction of thetransformed parity check matrix illustrated in FIG. 132.

Data (messages v_(i) from variable nodes) which corresponds to thepositions of is in the first to fifth rows of the transformed paritycheck matrix H′ illustrated in FIG. 132 is stored in the FIFO 300 ₁ suchthat each row is filled with data in the lateral direction (0 isignored). That is, when a j-th row and an i-th column are represented as(j, i), data corresponding to the positions of is in a 5×5 unit matrixfrom (1, 1) to (5, 5) of the transformed parity check matrix H′ isstored in the storage region in the first stage of the FIFO 300 ₁. Datawhich corresponds to the positions of is in a shifted matrix (a shiftedmatrix obtained by cyclically shifting the 5×5 unit matrix to the rightby 3) from (1, 21) to (5, 25) of the transformed parity check matrix H′is stored in the storage region in the second stage. Similarly, data isstored in the storage regions in the third to eighth stages so as to beassociated with the transformed parity check matrix H′. Data whichcorresponds to the positions of is in a shifted matrix (a shifted matrixobtained by substituting 1 in the first row of the 5×5 unit matrix with0 and cyclically shifting the unit matrix to the left by 1) from (1, 86)to (5, 90) of the transformed parity check matrix H′ is stored in thestorage region in the ninth stage.

Data which corresponds to the positions of is in the sixth to tenth rowsof the transformed parity check matrix H′ illustrated in FIG. 132 isstored in the FIFO 300 ₂. That is, data which corresponds to thepositions of is in a first shifted matrix forming a sum matrix (a summatrix which is the sum of the first shifted matrix obtained bycyclically shifting the 5×5 unit matrix to the right by 1 and a secondshifted matrix obtained by cyclically shifting the 5×5 unit matrix tothe right by 2) from (6, 1) to (10, 5) of the transformed parity checkmatrix H′ is stored in the storage region in the first stage of the FIFO300 ₂. In addition, data which corresponds to the positions of 1 s inthe second shifted matrix forming the sum matrix from (6, 1) to (10, 5)of the transformed parity check matrix H′ is stored in the storageregion in the second stage.

That is, when a constitutive matrix having a weight of 2 or greater isrepresented in the form of the sum of two or more of a P×P unit matrixhaving a weight of 1, a quasi unit matrix obtained by substituting oneor more of elements “1” in the unit matrix with 0, and a shifted matrixobtained by cyclically shifting the unit matrix or the quasi unitmatrix, data corresponding to the positions of is in the unit matrixhaving a weight of 1, the quasi unit matrix, or the shifted matrix(messages corresponding to edges belonging to the unit matrix, the quasiunit matrix, or the shifted matrix) is stored at the same address (thesame FIFO among the FIFOs 300 ₁ to 300 ₆).

Similarly, data is stored in the storage regions in the third to ninthstages so as to be associated with the transformed parity check matrixH′.

Similarly, data is stored in the FIFOs 300 ₃ to 300 ₆ so as to beassociated with the transformed parity check matrix H′.

The edge data storage memory 304 includes 18 FIFOs 304 ₁ to 304 ₁₈ ofwhich the number is obtained by dividing the number of columns 90 of thetransformed parity check matrix H′ by the number of columns 5 (the unitsize P) of the constitutive matrix. A FIFO 304 _(x) (x=1, 2, . . . , 18)includes storage regions in a plurality of stages. Messagescorresponding to five edges of which the number is equal to the numberof rows and the number of columns (the unit size P) in the constitutivematrix can be simultaneously read and written from and to the storageregion in each stage.

Data (messages u_(j) from check nodes) which corresponds to thepositions of is in the first to fifth rows of the transformed paritycheck matrix H′ illustrated in FIG. 132 is stored in the FIFO 304 ₁ suchthat each column is filled with data in the longitudinal direction (0 isignored). That is, data corresponding to the positions of 1s in a 5×5unit matrix from (1, 1) to (5, 5) of the transformed parity check matrixH′ is stored in the storage region in the first stage of the FIFO 304 ₁.Data which corresponds to the positions of is in a first shifted matrixforming a sum matrix (a sum matrix which is the sum of the first shiftedmatrix obtained by cyclically shifting the 5×5 unit matrix to the rightby 1 and a second shifted matrix obtained by cyclically shifting the 5×5unit matrix to the right by 2) from (6, 1) to (10, 5) of the transformedparity check matrix H′ is stored in the storage region in the secondstage. In addition, data which corresponds to the positions of is in thesecond shifted matrix forming the sum matrix from (6, 1) to (10, 5) ofthe transformed parity check matrix H′ is stored in the storage regionin the third stage.

That is, when a constitutive matrix having a weight of 2 or more isrepresented in the form of the sum of two or more of a P×P unit matrixhaving a weight of 1, a quasi unit matrix obtained by substituting oneor more of elements “1” in the unit matrix with 0, and a shifted matrixobtained by cyclically shifting the unit matrix or the quasi unitmatrix, data corresponding to the positions of is in the unit matrixhaving a weight of 1, the quasi unit matrix, or the shifted matrix(messages corresponding to edges belonging to the unit matrix, the quasiunit matrix, or the shifted matrix) is stored at the same address (thesame FIFO among the FIFOs 304 ₁ to 304 ₁₈).

Similarly, data is stored in the storage regions in the fourth and fifthstages so as to be associated with the transformed parity check matrixH′. The number of stages of the storage regions in the FIFO 304 ₁ is 5that is the maximum number of is (Hamming weight) in the row directionin the first to fifth columns of the transformed parity check matrix H′.

Similarly, data is stored in the FIFOs 304 ₂ and 304 ₃ so as to beassociated with the transformed parity check matrix H′ and the length(the number of stages) of each of the FIFOs 304 ₂ and 304 ₃ is 5.Similarly, data is stored in the FIFOs 304 ₄ to 304 ₁₂ so as to beassociated with the transformed parity check matrix H′ and the length ofeach of the FIFOs 304 ₄ to 304 ₁₂ is 3. Similarly, data is stored in theFIFOs 304 ₁₃ to 304 ₁₈ so as to be associated with the transformedparity check matrix H′ and the length of each of the FIFOs 304 ₁₃ to 304₁₈ is 2.

Next, the operation of the decoding device illustrated in FIG. 133 willbe described.

The edge data storage memory 300 includes six FIFOs 300 ₁ to 300 ₆,selects a FIFO in which data is to be stored from the FIFOs 300 ₁ to 300₆, according to information (matrix data) D312 indicating to which rowof the transformed parity check matrix H′ illustrated in FIG. 132 fivemessages D311 supplied from a cyclic shift circuit 308 in the previousstage belong, and collectively stores the five messages D311 in theselected FIFO in order. In addition, when reading data, the edge datastorage memory 300 sequentially reads five messages D300 ₁ from the FIFO300 ₁ and supplies the five messages D300 ₁ to a selector 301 in thenext stage. After ending the reading of the messages from the FIFO 300₁, the edge data storage memory 300 sequentially reads messages from theFIFOs 300 ₂ to 300 ₆ and supplies the messages to the selector 301.

The selector 301 selects five messages from the FIFO from which data iscurrently being read among the FIFOs 300 ₁ to 300 ₆, according to aselection signal D301, and supplies the selected messages as messagesD302 to the check node calculation unit 302.

The check node calculation unit 302 includes five check node calculators302 ₁ to 302 ₅, performs a check node operation according to Formula(7), using the messages D302 (D302 ₁ to D302 ₅) (messages v_(i) inFormula (7)) supplied through the selector 301, and supplies fivemessages D303 (D303 ₁ to D303 ₅) (messages u_(j) in Formula (7))obtained by the check node operation to a cyclic shift circuit 303.

The cyclic shift circuit 303 cyclically shifts the five messages D303 ₁to D303 ₅ calculated by the check node calculation unit 302, on thebasis of information (matrix data) D305 indicating how many unitmatrices (or quasi unit matrices) in which the corresponding edges serveas bases in the transformed parity check matrix H′ are cyclicallyshifted, and supplies the result as messages D304 to the edge datastorage memory 304.

The edge data storage memory 304 includes 18 FIFOs 304 ₁ to 304 ₁₈,selects a FIFO in which data is to be stored from the FIFOs 304 ₁ to 304₁₈, according to information D305 indicating to which row of thetransformed parity check matrix H′ the five messages D304 supplied fromthe cyclic shift circuit 303 in the previous stage belong, andcollectively stores the five messages D304 in the selected FIFO inorder. In addition, when reading data, the edge data storage memory 304sequentially reads five messages D306 ₁ from the FIFO 304 ₁ and suppliesthe five messages D306 ₁ to a selector 305 in the next stage. Afterending the reading of the messages from the FIFO 304 ₁, the edge datastorage memory 304 sequentially reads messages from the FIFOs 304 ₂ to304 ₁₈ and supplies the messages to the selector 305.

The selector 305 selects five messages from the FIFO from which data iscurrently being read among the FIFOs 304 ₁ to 304 ₁₈, according to aselection signal D307, and supplies the selected messages as messagesD308 to the variable node calculation unit 307 and the decoding wordcalculation unit 309.

The received data rearrangement unit 310 rearranges the LDPC code D313corresponding to the parity check matrix H illustrated in FIG. 130,which is received through the communication path 13, using the columnpermutation represented by Formula (12), and supplies the LDPC code asreceived data D314 to the received data memory 306. The received datamemory 306 calculates a reception log likelihood ratio (LLR) from thereceived data D314 supplied from the received data rearrangement unit310, stores the reception LLR, and supplies each set of five receptionLLRs as a reception value D309 to the variable node calculation unit 307and the decoding word calculation unit 309.

The variable node calculation unit 307 includes five variable nodecalculators 307 ₁ to 307 ₅, performs a variable node operation accordingto Formula (1), using the messages D308 (D308 ₁ to D308 ₅) (messagesu_(j) in Formula (1)) which are supplied through the selector 305 andthe five reception values D309 (reception values u_(0i) in Formula (1))which are supplied from the received data memory 306, and suppliesmessages D310 (D310 ₁ to D310 ₅) (messages v_(i) in Formula (1))obtained by the operation to the cyclic shift circuit 308.

The cyclic shift circuit 308 cyclically shifts the messages D310 ₁ toD310 ₅ calculated by the variable node calculation unit 307, on thebasis of information indicating how many unit matrices (or quasi unitmatrices) in which the corresponding edges serve as bases in thetransformed parity check matrix H′ are cyclically shifted, and suppliesthe result as messages D311 to the edge data storage memory 300.

The above-mentioned operation can be performed in one cycle to decode(perform the variable node operation and the check node operation) theLDPC code once. In the decoding device illustrated in FIG. 133, afterthe LDPC code is decoded a predetermined number of times, the decodingword calculation unit 309 and the decoded data rearrangement unit 311calculate a final decoding result and output the decoding result.

That is, the decoding word calculation unit 309 includes five decodingword calculators 309 ₁ to 309 ₅, calculates a decoding result (decodingword) on the basis of Formula (5) as a final stage among a plurality ofdecoding stages, using the five messages D308 (D308 ₁ to D308 ₅)(messages u_(j) in Formula (5)) which are output from the selector 305and the five reception values D309 (reception values u_(0i) in Formula(5)) which are supplied from the received data memory 306, and suppliesdecoded data D315 as the decoding result to the decoded datarearrangement unit 311.

The decoded data rearrangement unit 311 performs inverse permutation ofthe column permutation represented by Formula (12) for the decoded dataD315 which is supplied from the decoding word calculation unit 309 torearrange the order of the data and outputs the decoded data as a finaldecoding result D316.

As described above, it is possible to use an architecture in which oneor both of row permutation and column permutation are performed for theparity check matrix (original parity check matrix) to transform theparity check matrix into a parity check matrix (transformed parity checkmatrix) that can be represented by a combination of a P×P unit matrix, aquasi unit matrix obtained by substituting one or more of elements “1”of the unit matrix with 0, a shifted matrix obtained by cyclicallyshifting the unit matrix or the quasi unit matrix, a sum matrix which isthe sum of two or more of the unit matrix, the quasi unit matrix, andthe shifted matrix, and a P×P zero matrix, that is, a combination ofconstitutive matrices. According to the architecture, the check nodeoperation and the variable node operation can be simultaneouslyperformed P times which are less than the number of rows or the numberof columns of the parity check matrix, in order to decode the LDPC code.When the architecture in which the node operations (the check nodeoperation and the variable node operation) are simultaneously performedP times which are less than the number of rows or the number of columnsof the parity check matrix is used, an operation frequency can be keptin a feasible range and decoding can be repeated a number of times, ascompared to a case in which the number of node operations that aresimultaneously performed is equal to the number of rows or the number ofcolumns of the parity check matrix.

The LDPC decoder 166 forming the receiving device 12 illustrated in FIG.127 simultaneously performs the check node operation and the variablenode operation P times to perform LDPC decoding, for example, similarlyto the decoding device illustrated in FIG. 133.

That is, for simplicity of explanation, assuming that the parity checkmatrix of the LDPC code which is output from the LDPC encoder 115forming the transmitting device 11 illustrated in FIG. 8 is, forexample, the parity check matrix H illustrated in FIG. 130 in which theparity matrix has a dual diagonal structure, the parity interleaver 23of the transmitting device 11 performs parity interleaving whichinterleaves the (K+qx+y+1)-th code bit into the position of the(K+Py+x+1)-th code bit for an LDPC code in which the information lengthK is 60, the unit size P is 5, and the divisor q (=M/P) of the paritylength M is 6.

As described above, since the parity interleaving corresponds to thecolumn permutation represented by Formula (12), the LDPC decoder 166does not need to perform the column permutation represented by Formula(12).

Therefore, in the receiving device 12 illustrated in FIG. 127, asdescribed above, the group-wise deinterleaver 55 supplies the LDPC codewhich has not been subjected to parity deinterleaving, that is, the LDPCcode which has been subjected to the column permutation represented byFormula (12), to the LDPC decoder 166 and the LDPC decoder 166 performsthe same process as the decoding device illustrated in FIG. 133 exceptthat the column permutation represented by Formula (12) is notperformed.

That is, FIG. 134 is a diagram illustrating an example of the structureof the LDPC decoder 166 illustrated in FIG. 127.

In FIG. 134, the LDPC decoder 166 has the same structure as the decodingdevice illustrated in FIG. 133 except that it does not include thereceived data rearrangement unit 310 illustrated in FIG. 133 andperforms the same process as the decoding device illustrated in FIG. 133except that the column permutation represented by Formula (12) is notperformed. Therefore, the description thereof will not be repeated.

As described above, since the LDPC decoder 166 can be configured withoutthe received data rearrangement unit 310, the size of the LDPC decoder166 can be smaller than that of the decoding device illustrated in FIG.133.

For simplicity of illustration, in FIGS. 130 to 134, the code length Nof the LDPC code is 90, the information length K is 60, the unit size(the number of rows and the number of columns of the constitutivematrix) P is 5, and the divisor q (=M/P) of the parity length M is 6.However, the code length N, the information length K, the unit size P,and the divisor q (=M/P) are not limited to the above-mentioned values.

That is, in the transmitting device 11 illustrated in FIG. 8, the LDPCencoder 115 outputs, for example, an LDPC code having a code length N of64800 or 16200, an information length K of N−Pq (=N−M), a unit size P of360, and a divisor q of M/P. The LDPC decoder 166 illustrated in FIG.134 can be applied to a case in which the check node operation and thevariable node operation are simultaneously performed P times for theLDPC code to perform LDPC decoding.

When a parity portion of the decoding result is unnecessary and only theinformation bits of the decoding result are output after the LDPC codeis decoded by the LDPC decoder 166, the LDPC decoder 166 can beconfigured without the decoded data rearrangement unit 311.

<Example of Structure of Block Deinterleaver 54>

FIG. 135 is a block diagram illustrating an example of the structure ofthe block deinterleaver 54 illustrated in FIG. 128.

The block deinterleaver 54 has the same structure as the blockinterleaver 25 described in FIG. 93.

Therefore, the block deinterleaver 54 has a storage region which iscalled part 1 and a storage region which is called part 2. Each of parts1 and 2 includes C columns which are arranged in the row direction andof which the number is equal to the number of bits m of a symbol. Eachof the columns functions as a storage region which stores one bit in therow direction and stores a predetermined number of bits in the columndirection.

The block deinterleaver 54 writes and reads an LDPC code to and fromparts 1 and 2 to perform block deinterleaving.

However, in block deinterleaving, the LDPC code (symbol) is written inthe order in which the LDPC code is read by the block interleaver 25illustrated in FIG. 93.

In addition, in block deinterleaving, the LDPC code is read in the orderin which the LDPC code is written by the block interleaver 25illustrated in FIG. 93.

That is, in the block interleaving performed by the block interleaver 25illustrated in FIG. 93, the LDPC code is written to parts 1 and 2 in thecolumn direction and is read from parts 1 and 2 in the row direction.However, in the block deinterleaving performed by the blockdeinterleaver 54 illustrated in FIG. 135, the LDPC code is written toparts 1 and 2 in the row direction and is read from parts 1 and 2 in thecolumn direction.

<Another Example of Structure of Bit Deinterleaver 165>

FIG. 136 is a block diagram illustrating another example of thestructure of the bit deinterleaver 165 illustrated in FIG. 127.

In FIG. 136, portions corresponding to those illustrated in FIG. 128 aredenoted by the same reference numerals and the description thereof willbe appropriately omitted.

That is, the bit deinterleaver 165 illustrated in FIG. 136 has the samestructure as that illustrated in FIG. 128 except that it newly includesa parity deinterleaver 1011.

In FIG. 136, the bit deinterleaver 165 includes the block deinterleaver54, the group-wise deinterleaver 55, and the parity deinterleaver 1011and performs bit deinterleaving for the code bits of the LDPC codetransmitted from the demapper 164.

That is, the block deinterleaver 54 performs block deinterleaving (aninverse process of block interleaving) corresponding to the blockinterleaving performed by the block interleaver 25 of the transmittingdevice 11, that is, block deinterleaving which returns the positions ofthe code bits rearranged by the block interleaving to the originalpositions, for the LDPC code transmitted from the demapper 164 andsupplies the LDPC code obtained by the block deinterleaving to thegroup-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleavingcorresponding to the group-wise interleaving which is performed as arearrangement process by the group-wise interleaver 24 of thetransmitting device 11 for the LDPC code transmitted from the blockdeinterleaver 54.

The LDPC code obtained by the group-wise deinterleaving is supplied fromthe group-wise deinterleaver 55 to the parity deinterleaver 1011.

The parity deinterleaver 1011 performs parity deinterleaving (an inverseprocess of parity interleaving) corresponding to the parity interleavingperformed by the parity interleaver 23 of the transmitting device 11,that is, parity deinterleaving that returns the code bits of the LDPCcode, of which the sequence has been changed by the parity interleaving,to the original arrangement, for the code bits which have been subjectedto the group-wise deinterleaving by the group-wise deinterleaver 55.

The LDPC code obtained by the parity deinterleaving is supplied from theparity deinterleaver 1011 to the LDPC decoder 166.

Therefore, in the bit deinterleaver 165 illustrated in FIG. 136, theLDPC code that has been subjected to block deinterleaving, group-wisedeinterleaving, and parity deinterleaving, that is, the LDPC codeobtained by LDPC coding using the parity check matrix H, is supplied tothe LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding for the LDPC codetransmitted from the bit deinterleaver 165, using the parity checkmatrix H which has been used for LDPC coding by the LDPC encoder 115 ofthe transmitting device 11. That is, the LDPC decoder 166 performs LDPCdecoding for the LDPC code transmitted from the bit deinterleaver 165,using the parity check matrix H (based on the DVB method) which has beenused for LDPC coding by the LDPC encoder 115 of the transmitting device11 or the transformed parity check matrix obtained by performing atleast column permutation corresponding to parity interleaving for theparity check matrix H (for the ETRI method, the parity check matrix(FIG. 28) obtained by performing column permutation for the parity checkmatrix (FIG. 27) used for LDPC coding or the transformed parity checkmatrix (FIG. 29) obtained by performing row permutation for the paritycheck matrix (FIG. 27) used for LDPC coding).

Here, in FIG. 136, the LDPC code obtained by LDPC coding using theparity check matrix H is supplied from (the parity deinterleaver 1011of) the bit deinterleaver 165 to the LDPC decoder 166. Therefore, whenLDPC decoding is performed for the LDPC code, using the parity checkmatrix H (based on the DVB method) which has been used for LDPC codingby the LDPC encoder 115 of the transmitting device 11 (for the ETRImethod, the parity check matrix (FIG. 28) obtained by performing columnpermutation for the parity check matrix (FIG. 27) which has been usedfor LDPC coding), the LDPC decoder 166 can be a decoding device whichperforms LDPC decoding using, for example, a full serial decoding methodthat sequentially calculates messages (a check node message and avariable node message) for each node, or a decoding device whichperforms LDPC decoding using a full parallel decoding method thatcalculates messages for all nodes at the same time (in parallel).

In addition, when the LDPC decoder 166 performs LDPC decoding for theLDPC code, using the transformed parity check matrix (for the ETRImethod, the transformed parity check matrix (FIG. 29) obtained byperforming row permutation for the parity check matrix (FIG. 27) whichhas been used for LDPC coding) obtained by performing at least columnpermutation corresponding to parity interleaving for the parity checkmatrix H (based on the DVB method) which has been used for LDPC codingby the LDPC encoder 115 of the transmitting device 11, the LDPC decoder166 can be a decoding device (FIG. 133) that has an architecture whichsimultaneously performs the check node operation and the variable nodeoperation P times (or a divisor of P other than 1) and includes thereceived data rearrangement unit 310 which performs the same columnpermutation as the column permutation (parity interleaving) forobtaining the transformed parity check matrix for the LDPC code torearrange the code bits of the LDPC code. In FIG. 136, for convenienceof explanation, the block deinterleaver 54 which performs blockdeinterleaving, the group-wise deinterleaver 55 which performsgroup-wise deinterleaving, and the parity deinterleaver 1011 whichperforms parity deinterleaving are separately provided. However, two ormore of the block deinterleaver 54, the group-wise deinterleaver 55, andthe parity deinterleaver 1011 can be integrally provided, similarly tothe parity interleaver 23, the group-wise interleaver 24, and the blockinterleaver 25 of the transmitting device 11.

<Example of Structure of Receiving System>

FIG. 137 is a block diagram illustrating a first example of thestructure of a receiving system to which the receiving device 12 can beapplied.

In FIG. 137, the receiving system includes an acquisition unit 1101, atransmission path decoding processing unit 1102, and an informationsource decoding processing unit 1103.

The acquisition unit 1101 acquires a signal including an LDPC code whichis obtained by performing at least LDPC coding for LDPC target data,such as image data or audio data of a program, through a transmissionpath (communication path) (not illustrated), such as a digitalterrestrial broadcasting network, a digital satellite broadcastingnetwork, a CATV network, the Internet, or other networks, and suppliesthe signal to the transmission path decoding processing unit 1102.

Here, when the signal acquired by the acquisition unit 1101 is broadcastfrom a broadcasting station through, for example, terrestrial waves,satellite waves, or a cable television (CATV) network, the acquisitionunit 1101 includes, for example, a tuner and a set-top box. In addition,when the signal acquired by the acquisition unit 1101 is transmittedfrom, for example, a web server in a multicast manner as in an Internetprotocol television (IPTV) network, the acquisition unit 1101 includes anetwork interface (I/F) such as a network interface card (NIC).

The transmission path decoding processing unit 1102 corresponds to thereceiving device 12. The transmission path decoding processing unit 1102performs a transmission path decoding process which includes at least aprocess of correcting an error occurring in the transmission path forthe signal acquired by the acquisition unit 1101 through thetransmission path and supplies a signal obtained by the process to theinformation source decoding processing unit 1103.

That is, the signal acquired by the acquisition unit 1101 through thetransmission path is a signal obtained by performing at least errorcorrection coding for correcting an error occurring in the transmissionpath. The transmission path decoding processing unit 1102 performs atransmission path decoding process, such as an error correction process,for the signal.

Examples of the error correction coding include LDPC coding and BCHcoding. Here, at least the LDPC coding is performed as the errorcorrection coding.

The transmission path decoding process includes a process ofdemodulating a modulated signal.

The information source decoding processing unit 1103 performs aninformation source decoding process including at least a process ofdecompressing compressed information into original information for thesignal that has been subjected to the transmission path decodingprocess.

That is, in some cases, compression coding which compresses informationin order to reduce the amount of data, such as image data or audio data,as information is performed for the signal to be acquired by theacquisition unit 1101 through the transmission path. In this case, theinformation source decoding processing unit 1103 performs an informationsource decoding process, such as a process (decompression process) ofdecompressing compressed information into the original information, forthe signal that has been subjected to the transmission path decodingprocess.

When the acquisition unit 1101 acquires the signal which has not beensubjected to the compression coding through the transmission path, theinformation source decoding processing unit 1103 does not perform theprocess of decompressing compressed information into the originalinformation.

Here, the decompress process is, for example, MPEG decoding. Inaddition, in some cases, the transmission path decoding processincludes, for example, descrambling in addition to the decompressprocess.

In the receiving system having the above-mentioned structure, theacquisition unit 1101 acquires a signal which is obtained bysequentially performing compression coding, such as MPEG coding, anderror correction coding, such as LDPC coding, for image data or audiodata through a transmission path and supplies the signal to thetransmission path decoding processing unit 1102.

The transmission path decoding processing unit 1102 performs, forexample, the same process as the receiving device 12 as the transmissionpath decoding process for the signal from the acquisition unit 1101 andsupplies the processed signal to the information source decodingprocessing unit 1103.

The information source decoding processing unit 1103 performs aninformation source decoding process, such as MPEG decoding, for thesignal from the transmission path decoding processing unit 1102 andoutputs images or sounds obtained by the process.

The receiving system illustrated in FIG. 137 can be applied to, forexample, a television tuner that receives television broadcasting asdigital broadcasting.

The acquisition unit 1101, the transmission path decoding processingunit 1102, and the information source decoding processing unit 1103 maybe provided as independent devices (hardware (for example, integratedcircuits (ICs)) or software modules).

In addition, for the acquisition unit 1101, the transmission pathdecoding processing unit 1102, and the information source decodingprocessing unit 1103, a set of the acquisition unit 1101 and thetransmission path decoding processing unit 1102, a set of thetransmission path decoding processing unit 1102 and the informationsource decoding processing unit 1103, and a set of the acquisition unit1101, the transmission path decoding processing unit 1102, and theinformation source decoding processing unit 1103 may be provided asindependent devices.

FIG. 138 is a block diagram illustrating a second example of thestructure of the receiving system to which the receiving device 12 canbe applied.

In FIG. 138, portions corresponding to those illustrated in FIG. 137 aredenoted by the same reference numerals and the description thereof willbe appropriately omitted below.

A receiving system illustrated in FIG. 138 is similar to the receivingsystem illustrated in FIG. 137 in that it includes the acquisition unit1101, the transmission path decoding processing unit 1102, and theinformation source decoding processing unit 1103 and differs from thereceiving system illustrated in FIG. 137 in that it newly includes anoutput unit 1111.

The output unit 1111 is, for example, a display device which displaysimages or a speaker which outputs sounds and outputs images or sounds assignals output from the information source decoding processing unit1103. That is, the output unit 1111 displays images or outputs sounds.

The receiving system illustrated in FIG. 138 can be applied to, forexample, a television receiver (TV) which receives televisionbroadcasting as digital broadcasting or a radio receiver which receivesradio broadcasting.

When the acquisition unit 1101 receives the signal which has not beensubjected to compression coding, the signal output by the transmissionpath decoding processing unit 1102 is supplied to the output unit 1111.

FIG. 139 is a block diagram illustrating a third example of thestructure of the receiving system to which the receiving device 12 canbe applied.

In FIG. 139, portions corresponding to those illustrated in FIG. 137 aredenoted by the same reference numerals and the description thereof willbe appropriately omitted below.

A receiving system illustrated in FIG. 139 is similar to the receivingsystem illustrated in FIG. 137 in that it includes the acquisition unit1101 and the transmission path decoding processing unit 1102.

However, the receiving system illustrated in FIG. 139 differs from thereceiving system illustrated in FIG. 137 in that it does not include theinformation source decoding processing unit 1103 and newly includes arecording unit 1121.

The recording unit 1121 records (stores) the signal (for example, a MPEGTS packet) output by the transmission path decoding processing unit 1102on a recording (storage) medium, such as an optical disc, a hard disk(magnetic disk), or a flash memory.

The receiving system illustrated in FIG. 139 can be applied to, forexample, a recorder which records television broadcasting.

In FIG. 139, the receiving system may include the information sourcedecoding processing unit 1103 and the recording unit 1121 may record asignal which has been subjected to an information source decodingprocess by the information source decoding processing unit 1103, thatis, images or sounds obtained by decoding.

<Embodiment of Computer>

The above-mentioned series of processes may be performed by hardware orsoftware. When the series of processes is performed by software, aprogram forming the software is installed in, for example, ageneral-purpose computer.

FIG. 140 illustrates an example of the structure of an embodiment of thecomputer in which a program for executing the series of processes isinstalled.

The program can be recorded in advance on a hard disk 705 or a ROM 703serving as a recording medium which is provided in the computer.

Alternatively, the program can be temporarily or permanently stored(recorded) in a removable recording medium 711, such as a flexible disk,a compact disc read only memory (CD-ROM), a magneto-optical (MO) disc, adigital versatile disc (DVD), a magnetic disk, or a semiconductormemory. The removable recording medium 711 can be provided as so-calledpackage software.

In addition to being installed in the computer from the removablerecording medium 711, the program can be wirelessly transmitted from adownload site to the computer through a satellite for digital satellitebroadcasting or can be transmitted from the download site to thecomputer through a network, such as a local area network (LAN) or theInternet, in a wired manner. In the computer, the transmitted programcan be received by a communication unit 708 and can be installed in thebuilt-in hard disk 705.

The computer includes a central processing unit (CPU) 702. The CPU 702is connected to an input/output interface 710 through a bus 701. When acommand which is input by the user through an input unit 707 including,for example, a keyboard, a mouse, and a microphone is received throughthe input/output interface 710, the CPU 702 executes a program stored inthe read only memory (ROM) 703 in response to the command.Alternatively, the CPU 702 loads a program which has been stored in thehard disk 705, a program which has been transmitted from a satellite ora network, received by the communication unit 708, and then installed inthe hard disk 705, or a program which has been read from the removablerecording medium 711 inserted into a drive 709 and then installed in thehard disk 705 to a random access memory (RAM) 704 and executes theprogram. In this way, the CPU 702 performs the processes correspondingto the above-described flowcharts or the processes performed by thestructures of the above-described block diagrams. Then, the CPU 702outputs the processing result from an output unit 706 including, forexample, a liquid crystal display (LCD) or a speaker, or transmits theprocessing result from the communication unit 708 and records theprocessing result on the hard disk 705 through the input/outputinterface 710, if necessary.

In the specification, processing steps for describing a program whichcauses a computer to perform various types of processes are notnecessarily performed in time series in the order described asflowcharts and include processes (for example, parallel processing orprocessing by an object) which are performed separately or in parallel.

In addition, the program may be processed by one computer or may bedistributedly processed by a plurality of computers. Further, theprogram may be transmitted to a remote computer and then executed by theremote computer.

The embodiment of the present technology is not limited to theabove-described embodiments and can be modified in various ways, withoutdeparting from the scope and spirit of the present technology.

That is, for example, (the parity check matrix initial value table of)the above-mentioned new LDPC code can be used when the communicationpath 13 (FIG. 7) is any one of a satellite channel, a terrestrialchannel, a cable (wired line), and other channels. Further, the new LDPCcode can be used in data transmission other than digital broadcasting.

In addition, the above-mentioned GW pattern can be applied to codesother than the new LDPC code. Furthermore, a modulation method to whichthe above-mentioned GW pattern is applied is not limited to 16QAM,64QAM, 256QAM, and 1024QAM.

The effects described in the specification are illustrative. Theinvention is not limited to the above-mentioned effects and may haveother effects.

REFERENCE SIGNS LIST

-   11 Transmitting device-   12 Receiving device-   23 Parity interleaver-   24 Group-wise interleaver-   25 Block interleaver-   54 Block deinterleaver-   55 Group-wise deinterleaver-   111 Mode adaptation/multiplexer-   112 Padder-   113 BB scrambler-   114 BCH encoder-   115 LDPC encoder-   116 Bit interleaver-   117 Mapper-   118 Time interleaver-   119 SISO/MISO encoder-   120 Frequency interleaver-   121 BCH encoder-   122 LDPC encoder-   123 Mapper-   124 Frequency interleaver-   131 Frame builder/resource allocation unit-   132 OFDM generation unit-   151 OFDM processing unit-   152 Frame management unit-   153 Frequency deinterleaver-   154 Demapper-   155 LDPC decoder-   156 BCH decoder-   161 Frequency deinterleaver-   162 SISO/MISO decoder-   163 Time deinterleaver-   164 Demapper-   165 Bit deinterleaver-   166 LDPC decoder-   167 BCH decoder-   168 BB descrambler-   169 Null deletion unit-   170 Demultiplexer-   300 Edge data storage memory-   301 Selector-   302 Check node calculation unit-   303 Cyclic shift circuit-   304 Edge data storage memory-   305 Selector-   306 Received data memory-   307 Variable node calculation unit-   308 Cyclic shift circuit-   309 Decoding word calculation unit-   310 Received data rearrangement unit-   311 Decoded data rearrangement unit-   601 Coding processing unit-   602 Storage unit-   611 Coding rate setting unit-   612 Initial value table reading unit-   613 Parity check matrix generation unit-   614 Information bit reading unit-   615 Coding parity calculation unit-   616 Control unit-   701 Bus-   702 CPU-   703 ROM-   704 RAM-   705 Hard disk-   706 Output unit-   707 Input unit-   708 Communication unit-   709 Drive-   710 Input/output interface-   711 Removable recording medium-   1001 Inverse Reordering unit-   1002 Memory-   1011 Parity deinterleaver-   1101 Acquisition unit-   1101 Transmission path decoding processing unit-   1103 Information source decoding processing unit-   1111 Output unit-   1121 Recording unit

1. A method comprising: low density parity check (LDPC) coding data to be transmitted in a digital broadcast signal by a transmitting device on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 11/15 to generate an LDPC code word, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table, having each row indicating positions of elements “1” in corresponding 360 columns of the information matrix portion, includes the following, 696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912 444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268 401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157 1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205 542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241 15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209 0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237 3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953 1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273 1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262 2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195 2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263 3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123 26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266 904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259 7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253 4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204 24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220 88 11622 14705 15890 304 2026 2638 6018 1163 4268 11620 17232 9701 11785 14463 17260 4118 10952 12224 17006 3647 10823 11521 12060 1717 3753 9199 11642 2187 14280 17220 14787 16903 17061 381 3534 4294 3149 6947 8323 12562 16724 16881 7289 9997 15306 5615 13152 17260 5666 16926 17027 4190 7798 16831 4778 10629 17180 10001 13884 15453 6 2237 8203 7831 15144 15160 9186 17204 17243 9435 17168 17237 42 5701 17159 7812 14259 15715 39 4513 6658 38 9368 11273 1119 4785 17182 5620 16521 16729 16 6685 17242 210 3452 12383 466 14462 16250 10548 12633 13962 1452 6005 16453 22 4120 13684 5195 11563 16522 5518 16705 17201 12233 14552 15471 6067 13440 17248 8660 8967 17061 8673 12176 15051 5959 15767 16541 3244 12109 12414 31 15913 16323 3270 15686 16653 24 7346 14675 12 1531 8740 6228 7565 16667 16936 17122 17162 4868 8451 13183 3714 4451 16919 11313 13801 17132 17070 17191 17242 1911 11201 17186 14 17190 17254 11760 16008 16832 14543 17033 17278 16129 16765 17155 6891 15561 17007 12741 14744 17116 8992 16661 17277 1861 11130 16742 4822 13331 16192 13281 14027 14989 38 14887 17141 10698 13452 15674 4 2539 16877 857 17170 17249 11449 11906 12867 285 14118 16831 15191 17214 17242 39 728 16915 2469 12969 15579 16644 17151 17164 2592 8280 10448 9236 12431 17173 9064 16892 17233 4526 16146 17038 31 2116 16083 15837 16951 17031 5362 8382 16618 6137 13199 17221 2841 15068 17068 24 3620 17003 9880 15718 16764 1784 10240 17209 2731 10293 10846 3121 8723 16598 8563 15662 17088 13 1167 14676 29 13850 15963 3654 7553 8114 23 4362 14865 4434 14741 16688 8362 13901 17244 13687 16736 17232 46 4229 13394 13169 16383 16972 16031 16681 16952 3384 9894 12580 9841 14414 16165 5013 17099 17115 2130 8941 17266 6907 15428 17241 16 1860 17235 2151 16014 16643 14954 15958 17222 3969 8419 15116 31 15593 16984 11514 16605 17255; group-wise interleaving the LDPC code word in units of bit groups of 360 bits to generate a group-wise interleaved LDPC code word; wherein, in the group-wise interleaving, an (i+1)-th bit group from a head of the LDPC code word is indicated by a bit group i, and a sequence of bit groups 0 to 179 of the LDPC code word of 64800 bits is interleaved into a following sequence of bit groups 21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73, 100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10, 13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95, 86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82, 32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70, 91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131, 33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60, 67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179; mapping the group-wise interleaved LDPC code word to any one of 16 signal points which are determined by a modulation scheme in a unit of 4 bits; and transmitting the digital broadcast signal including the mapped group-wise interleaved LDPC code word, to a receiving device.
 2. The method of claim 1, wherein the parity check matrix has no cycle-4.
 3. The method of claim 1, wherein the modulation scheme employs non uniform constellations (NUCs).
 4. A receiving device comprising: a receiver configured to receive a digital broadcast signal including a mapped group-wise interleaved low density parity check (LDPC) code word from a transmitting device; and circuitry configured to process the mapped group-wise interleaved LDPC code word to obtain a group-wise interleaved LDPC code word, wherein each unit of 4 bits of the group-wise interleaved LDPC code word is mapped to one of 16 signal points of a modulation scheme, process the group-wise interleaved LDPC code word in units of bit groups of 360 bits to obtain an LDPC code word of a LDPC code, wherein an (i+1)-th bit group from a head of the LDPC code word of the LDPC code is indicated by a bit group i, the LDPC code word of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC code word has a following sequence of bit groups, 21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73, 100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10, 13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95, 86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82, 32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70, 91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131, 33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60, 67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179; decode the LDPC code word of the LDPC code to obtain a decoded LDPC code word, and process the decoded LDPC code word for presentation of the digital broadcast signal; wherein the LDPC code has a code length N of 64800 bits and a coding rate r of 11/15 and is based on a parity check matrix initial value table listed as follows, 696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912 444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268 401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157 1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205 542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241 15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209 0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237 3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953 1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273 1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262 2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195 2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263 3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123 26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266 904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259 7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253 4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204 24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220 88 11622 14705 15890 304 2026 2638 6018 1163 4268 11620 17232 9701 11785 14463 17260 4118 10952 12224 17006 3647 10823 11521 12060 1717 3753 9199 11642 2187 14280 17220 14787 16903 17061 381 3534 4294 3149 6947 8323 12562 16724 16881 7289 9997 15306 5615 13152 17260 5666 16926 17027 4190 7798 16831 4778 10629 17180 10001 13884 15453 6 2237 8203 7831 15144 15160 9186 17204 17243 9435 17168 17237 42 5701 17159 7812 14259 15715 39 4513 6658 38 9368 11273 1119 4785 17182 5620 16521 16729 16 6685 17242 210 3452 12383 466 14462 16250 10548 12633 13962 1452 6005 16453 22 4120 13684 5195 11563 16522 5518 16705 17201 12233 14552 15471 6067 13440 17248 8660 8967 17061 8673 12176 15051 5959 15767 16541 3244 12109 12414 31 15913 16323 3270 15686 16653 24 7346 14675 12 1531 8740 6228 7565 16667 16936 17122 17162 4868 8451 13183 3714 4451 16919 11313 13801 17132 17070 17191 17242 1911 11201 17186 14 17190 17254 11760 16008 16832 14543 17033 17278 16129 16765 17155 6891 15561 17007 12741 14744 17116 8992 16661 17277 1861 11130 16742 4822 13331 16192 13281 14027 14989 38 14887 17141 10698 13452 15674 4 2539 16877 857 17170 17249 11449 11906 12867 285 14118 16831 15191 17214 17242 39 728 16915 2469 12969 15579 16644 17151 17164 2592 8280 10448 9236 12431 17173 9064 16892 17233 4526 16146 17038 31 2116 16083 15837 16951 17031 5362 8382 16618 6137 13199 17221 2841 15068 17068 24 3620 17003 9880 15718 16764 1784 10240 17209 2731 10293 10846 3121 8723 16598 8563 15662 17088 13 1167 14676 29 13850 15963 3654 7553 8114 23 4362 14865 4434 14741 16688 8362 13901 17244 13687 16736 17232 46 4229 13394 13169 16383 16972 16031 16681 16952 3384 9894 12580 9841 14414 16165 5013 17099 17115 2130 8941 17266 6907 15428 17241 16 1860 17235 2151 16014 16643 14954 15958 17222 3969 8419 15116 31 15593 16984 11514 16605
 17255. 5. The receiving device of claim 4, wherein the LDPC code word of the LDPC code is encoded based on a parity check matrix of the LDPC code, the LDPC code word includes information bits and parity bits; the parity check matrix includes an information matrix part corresponding to the information bits and a parity matrix part corresponding to the parity bits, the information matrix part is represented by the parity check matrix initial value table, and each row of the parity check matrix initial value table indicates positions of elements “1” in corresponding 360 columns of the information matrix part corresponding to a subset of information bits used in calculating the parity bits.
 6. The receiving device of claim 5, wherein a row of the parity check matrix initial value table is represented by i and a length of the parity bits of the LDPC code word of the LDPC code is represented by M, a 2+360×(i−1)-th column of the parity check matrix is obtained by a cyclic shift of a 1+360×(i−1)-th column of the parity check matrix downward by q=M/360.
 7. The receiving device of claim 6, wherein for the 1+360×(i−1)-th column of the parity check matrix, an i-th row of the parity check matrix initial value table includes one or more values each representing a different row number of element 1 of the 1+360×(i−1)-th column of the parity check matrix, and for each column from the 2+360×(i−1)-th column to a 360×i-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix, an i-th row and j-th column value of the parity check matrix initial value table is represented as Hi, j and a row number of a j-th element 1 of a w-th column of the parity check matrix H is represented as Hw−j, the row number Hw−j of the element 1 of the w-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix is represented by the equation Hw−j=mod(Hi, j+mod((w−1), 360)×M/360, M).
 8. The receiving device of claim 5, wherein the parity matrix part is a lower bidiagonal matrix, in which elements of “1” are arranged in a step-wise fashion.
 9. The receiving device of claim 5, wherein the parity check matrix has no cycle-4.
 10. The receiving device of claim 5, wherein the parity check matrix of the LDPC code belongs to an ensemble in which a performance threshold being a ratio of signal power to noise power at which a bit error rate starts to decrease is a predetermined value or smaller is found by multi-edge type density evolution.
 11. A method comprising: receiving by a receiving device, a digital broadcast signal including a mapped group-wise interleaved low density parity check (LDPC) code word from a transmitting device; processing the mapped group-wise interleaved LDPC code word to obtain a group-wise interleaved LDPC code word, wherein each unit of 4 bits of the group-wise interleaved LDPC code word is mapped to one of 16 signal points of a modulation scheme; processing the group-wise interleaved LDPC code word in units of bit groups of 360 bits to obtain an LDPC code word of an LDPC code, wherein an (i+1)-th bit group from a head of the LDPC code word of the LDPC code is indicated by a bit group i, the LDPC code word of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC code word has a following sequence of bit groups, 21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73, 100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10, 13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95, 86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82, 32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70, 91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131, 33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60, 67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179; decoding the LDPC code word of the LDPC code to obtain a decoded LDPC code word, and processing the decoded LDPC code word for presentation of the digital broadcast signal; wherein the LDPC code has a code length N of 64800 bits and a coding rate r of 11/15 and is based on a parity check matrix initial value table listed as follows, 696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912 444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268 401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157 1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205 542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241 15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209 0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237 3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953 1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273 1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262 2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195 2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263 3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123 26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266 904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259 7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253 4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204 24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220 88 11622 14705 15890 304 2026 2638 6018 1163 4268 11620 17232 9701 11785 14463 17260 4118 10952 12224 17006 3647 10823 11521 12060 1717 3753 9199 11642 2187 14280 17220 14787 16903 17061 381 3534 4294 3149 6947 8323 12562 16724 16881 7289 9997 15306 5615 13152 17260 5666 16926 17027 4190 7798 16831 4778 10629 17180 10001 13884 15453 6 2237 8203 7831 15144 15160 9186 17204 17243 9435 17168 17237 42 5701 17159 7812 14259 15715 39 4513 6658 38 9368 11273 1119 4785 17182 5620 16521 16729 16 6685 17242 210 3452 12383 466 14462 16250 10548 12633 13962 1452 6005 16453 22 4120 13684 5195 11563 16522 5518 16705 17201 12233 14552 15471 6067 13440 17248 8660 8967 17061 8673 12176 15051 5959 15767 16541 3244 12109 12414 31 15913 16323 3270 15686 16653 24 7346 14675 12 1531 8740 6228 7565 16667 16936 17122 17162 4868 8451 13183 3714 4451 16919 11313 13801 17132 17070 17191 17242 1911 11201 17186 14 17190 17254 11760 16008 16832 14543 17033 17278 16129 16765 17155 6891 15561 17007 12741 14744 17116 8992 16661 17277 1861 11130 16742 4822 13331 16192 13281 14027 14989 38 14887 17141 10698 13452 15674 4 2539 16877 857 17170 17249 11449 11906 12867 285 14118 16831 15191 17214 17242 39 728 16915 2469 12969 15579 16644 17151 17164 2592 8280 10448 9236 12431 17173 9064 16892 17233 4526 16146 17038 31 2116 16083 15837 16951 17031 5362 8382 16618 6137 13199 17221 2841 15068 17068 24 3620 17003 9880 15718 16764 1784 10240 17209 2731 10293 10846 3121 8723 16598 8563 15662 17088 13 1167 14676 29 13850 15963 3654 7553 8114 23 4362 14865 4434 14741 16688 8362 13901 17244 13687 16736 17232 46 4229 13394 13169 16383 16972 16031 16681 16952 3384 9894 12580 9841 14414 16165 5013 17099 17115 2130 8941 17266 6907 15428 17241 16 1860 17235 2151 16014 16643 14954 15958 17222 3969 8419 15116 31 15593 16984 11514 16605
 17255. 12. The method of claim 11, wherein the LDPC code word of the LDPC code is encoded based on a parity check matrix of the LDPC code, the LDPC code word includes information bits and parity bits; the parity check matrix includes an information matrix part corresponding to the information bits and a parity matrix part corresponding to the parity bits, the information matrix part being represented by the parity check matrix initial value table, and each row of the parity check matrix initial value table indicates positions of elements “1” in corresponding 360 columns of the information matrix part corresponding to a subset of information bits used in calculating the parity bits.
 13. The method of claim 12, wherein a row of the parity check matrix initial value table is represented by i and a length of the parity bits of the LDPC code word of the LDPC code is represented by M, a 2+360×(i−1)-th column of the parity check matrix is obtained by a cyclic shift of a 1+360×(i−1)-th column of the parity check matrix downward by q=M/360.
 14. The method of claim 13, wherein for the 1+360×(i−1)-th column of the parity check matrix, an i-th row of the parity check matrix initial value table includes one or more values each representing a different row number of element 1 of the 1+360×(i−1)-th column of the parity check matrix, and for each column from the 2+360×(i−1)-th column to a 360×i-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix, an i-th row and j-th column value of the parity check matrix initial value table is represented as Hi, j and a row number of a j-th element 1 of a w-th column of the parity check matrix H is represented as Hw−j, the row number Hw-j of the element 1 of the w-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix is represented by the equation Hw−j=mod(Hi, j+mod((w−1), 360)×M/360, M).
 15. The method of claim 12, wherein the parity matrix part is a lower bidiagonal matrix, in which elements of “1” are arranged in a step-wise fashion.
 16. The method of claim 12, wherein the parity check matrix has no cycle-4.
 17. The method of claim 12, wherein the parity check matrix of the LDPC code belongs to an ensemble in which a performance threshold being a ratio of signal power to noise power at which a bit error rate starts to decrease is a predetermined value or smaller is found by multi-edge type density evolution.
 18. The method of claim 4, wherein the modulation scheme employs non uniform constellations (NUCs).
 19. A non-transitory computer readable medium including computer executable instructions which, when executed by a computer, cause the computer to perform a method comprising: receiving by a receiving device, a digital broadcast signal including a mapped group-wise interleaved low density parity check (LDPC) code word from a transmitting device; processing the mapped group-wise interleaved LDPC code word to obtain a group-wise interleaved LDPC code word, wherein each unit of 4 bits of the group-wise interleaved LDPC code word is mapped to one of 16 signal points of a modulation scheme; processing the group-wise interleaved LDPC code word in units of bit groups of 360 bits to obtain an LDPC code word of an LDPC code, wherein an (i+1)-th bit group from a head of the LDPC code word of the LDPC code is indicated by a bit group i, the LDPC code word of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC code word has a following sequence of bit groups, 0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107, 31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129, 52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97, 33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17, 15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130, 56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45, 78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96, 32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179; decoding the LDPC code word of the LDPC code to obtain a decoded LDPC code word, and processing the decoded LDPC code word for presentation of the digital broadcast signal; wherein the LDPC code has a code length N of 64800 bits and a coding rate r of 11/15 and is based on a parity check matrix initial value table listed as follows, 696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912 444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268 401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157 1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205 542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241 15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209 0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237 3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953 1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273 1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262 2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195 2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263 3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123 26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266 904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259 7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253 4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204 24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220 88 11622 14705 15890 304 2026 2638 6018 1163 4268 11620 17232 9701 11785 14463 17260 4118 10952 12224 17006 3647 10823 11521 12060 1717 3753 9199 11642 2187 14280 17220 14787 16903 17061 381 3534 4294 3149 6947 8323 12562 16724 16881 7289 9997 15306 5615 13152 17260 5666 16926 17027 4190 7798 16831 4778 10629 17180 10001 13884 15453 6 2237 8203 7831 15144 15160 9186 17204 17243 9435 17168 17237 42 5701 17159 7812 14259 15715 39 4513 6658 38 9368 11273 1119 4785 17182 5620 16521 16729 16 6685 17242 210 3452 12383 466 14462 16250 10548 12633 13962 1452 6005 16453 22 4120 13684 5195 11563 16522 5518 16705 17201 12233 14552 15471 6067 13440 17248 8660 8967 17061 8673 12176 15051 5959 15767 16541 3244 12109 12414 31 15913 16323 3270 15686 16653 24 7346 14675 12 1531 8740 6228 7565 16667 16936 17122 17162 4868 8451 13183 3714 4451 16919 11313 13801 17132 17070 17191 17242 1911 11201 17186 14 17190 17254 11760 16008 16832 14543 17033 17278 16129 16765 17155 6891 15561 17007 12741 14744 17116 8992 16661 17277 1861 11130 16742 4822 13331 16192 13281 14027 14989 38 14887 17141 10698 13452 15674 4 2539 16877 857 17170 17249 11449 11906 12867 285 14118 16831 15191 17214 17242 39 728 16915 2469 12969 15579 16644 17151 17164 2592 8280 10448 9236 12431 17173 9064 16892 17233 4526 16146 17038 31 2116 16083 15837 16951 17031 5362 8382 16618 6137 13199 17221 2841 15068 17068 24 3620 17003 9880 15718 16764 1784 10240 17209 2731 10293 10846 3121 8723 16598 8563 15662 17088 13 1167 14676 29 13850 15963 3654 7553 8114 23 4362 14865 4434 14741 16688 8362 13901 17244 13687 16736 17232 46 4229 13394 13169 16383 16972 16031 16681 16952 3384 9894 12580 9841 14414 16165 5013 17099 17115 2130 8941 17266 6907 15428 17241 16 1860 17235 2151 16014 16643 14954 15958 17222 3969 8419 15116 31 15593 16984 11514 16605
 17255. 20. The non-transitory computer readable medium of claim 19, wherein the modulation scheme employs non uniform constellations (NUCs). 